146:@0.054582:0.966558:0.078778:0.966558:0.078778:0.950778:0.054582:0.950778:0.000000:0.000000:0.000000
M.5.2.24. Aplicar la divisibilidad de números enteros, el cálculo del máximo común divisor y del mínimo común múltiplo de un conjunto de números enteros, y la resolución :@0.148948:0.943402:0.888344:0.943402:0.888344:0.933360:0.148948:0.933360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de ecuaciones lineales con dos incógnitas (con soluciones enteras no negativas) en la solución de problemas.:@0.148948:0.952203:0.618687:0.952203:0.618687:0.942161:0.148948:0.942161:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ecuación lineal con dos incógnitas. :@0.404235:0.117192:0.838557:0.117192:0.838557:0.072532:0.404235:0.072532:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Soluciones enteras:@0.404235:0.154911:0.627929:0.154911:0.627929:0.110251:0.404235:0.110251:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Divisibilidad en  . Aplicaciones:@0.404236:0.184548:0.655803:0.184548:0.655803:0.166865:0.404236:0.166865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Z:@0.532509:0.182936:0.545359:0.182936:0.545359:0.169489:0.532509:0.169489:0.000000
Definición :@0.404236:0.201718:0.491103:0.201718:0.491103:0.184772:0.404236:0.184772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean  ,      con   ≠ 0. Se dice que   divide a  , lo cual :@0.484322:0.201256:0.895901:0.201256:0.895901:0.184758:0.484322:0.184758:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m n:@0.527322:0.201371:0.557568:0.201371:0.557568:0.184902:0.527322:0.184902:0.000000:0.000000:0.000000
:@0.560920:0.200737:0.575572:0.200737:0.575572:0.187364:0.560920:0.187364:0.000000
Z :@0.578913:0.200169:0.595812:0.200169:0.595812:0.187306:0.578913:0.187306:0.000000:0.000000
m:@0.625207:0.201371:0.640003:0.201371:0.640003:0.184902:0.625207:0.184902:0.000000
m:@0.754824:0.201371:0.769619:0.201371:0.769619:0.184902:0.754824:0.184902:0.000000
n:@0.830594:0.201371:0.839957:0.201371:0.839957:0.184902:0.830594:0.184902:0.000000
se escribe :@0.404235:0.218606:0.476978:0.218606:0.476978:0.202109:0.404235:0.202109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m|n:@0.476959:0.218722:0.505953:0.218722:0.505953:0.202253:0.476959:0.202253:0.000000:0.000000:0.000000
 si existe      , tal que   = :@0.505953:0.218606:0.700109:0.218606:0.700109:0.202109:0.505953:0.202109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.568141:0.218722:0.576387:0.218722:0.576387:0.202253:0.568141:0.202253:0.000000
:@0.580485:0.218088:0.595137:0.218088:0.595137:0.204714:0.580485:0.204714:0.000000
Z:@0.599256:0.217519:0.611547:0.217519:0.611547:0.204657:0.599256:0.204657:0.000000
n km:@0.671674:0.218722:0.722881:0.218722:0.722881:0.202253:0.671674:0.202253:0.000000:0.000000:0.000000:0.000000
. En tal caso, se dice que :@0.722862:0.218606:0.895937:0.218606:0.895937:0.202109:0.722862:0.202109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.404234:0.236073:0.413597:0.236073:0.413597:0.219604:0.404234:0.219604:0.000000
 se factoriza en la forma :@0.413597:0.235957:0.585693:0.235957:0.585693:0.219459:0.413597:0.219459:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
km:@0.585693:0.236073:0.608484:0.236073:0.608484:0.219604:0.585693:0.219604:0.000000:0.000000
, y que   es un divisor de  . :@0.608484:0.235957:0.808552:0.235957:0.808552:0.219459:0.608484:0.219459:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.658497:0.236073:0.673292:0.236073:0.673292:0.219604:0.658497:0.219604:0.000000
n:@0.792292:0.236073:0.801655:0.236073:0.801655:0.219604:0.792292:0.219604:0.000000
Definición :@0.404234:0.268099:0.491101:0.268099:0.491101:0.251153:0.404234:0.251153:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean  ,       con   ≠ 0,   ≠ 0.:@0.484319:0.267637:0.707574:0.267641:0.707574:0.251143:0.484319:0.251139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.528899:0.267752:0.554040:0.267752:0.554040:0.251284:0.528899:0.251284:0.000000:0.000000:0.000000
:@0.558181:0.267122:0.572833:0.267122:0.572833:0.253749:0.558181:0.253749:0.000000
Z:@0.576975:0.266554:0.589266:0.266554:0.589266:0.253692:0.576975:0.253692:0.000000
a:@0.624503:0.267757:0.633480:0.267757:0.633480:0.251288:0.624503:0.251288:0.000000
b:@0.667965:0.267757:0.677232:0.267757:0.677232:0.251288:0.667965:0.251288:0.000000
1.:@0.404243:0.285209:0.416515:0.285209:0.416515:0.268494:0.404243:0.268494:0.000000:0.000000
  Un número       se dice divisor común de   y   si :@0.416515:0.284992:0.803584:0.284992:0.803584:0.268494:0.416515:0.268494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
d:@0.515288:0.285107:0.524458:0.285107:0.524458:0.268639:0.515288:0.268639:0.000000
:@0.528601:0.284473:0.543253:0.284473:0.543253:0.271100:0.528601:0.271100:0.000000
Z:@0.547395:0.283905:0.559687:0.283905:0.559687:0.271043:0.547395:0.271043:0.000000
+:@0.559687:0.278639:0.565988:0.278639:0.565988:0.269021:0.559687:0.269021:0.000000
a b d|a d|b:@0.750893:0.285107:0.865945:0.285107:0.865945:0.268639:0.750893:0.268639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y :@0.826567:0.284992:0.842673:0.284992:0.842673:0.268494:0.826567:0.268494:0.000000:0.000000:0.000000
.:@0.865945:0.284992:0.868700:0.284992:0.868700:0.268494:0.865945:0.268494:0.000000
2.:@0.404236:0.302559:0.416508:0.302559:0.416508:0.285845:0.404236:0.285845:0.000000:0.000000
  El máximo común divisor de   y   es el número entero       que :@0.416508:0.302343:0.895915:0.302343:0.895915:0.285845:0.416508:0.285845:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.633163:0.302458:0.666396:0.302458:0.666396:0.285989:0.633163:0.285989:0.000000:0.000000:0.000000
c:@0.813600:0.302458:0.820786:0.302458:0.820786:0.285989:0.813600:0.285989:0.000000
:@0.824354:0.301824:0.839007:0.301824:0.839007:0.288451:0.824354:0.288451:0.000000
Z:@0.842588:0.301256:0.854879:0.301256:0.854879:0.288393:0.842588:0.288393:0.000000
+:@0.854879:0.295990:0.861180:0.295990:0.861180:0.286371:0.854879:0.286371:0.000000
verifica las condiciones siguientes::@0.427981:0.319693:0.667175:0.319693:0.667175:0.303196:0.427981:0.303196:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.404246:0.337044:0.408388:0.337044:0.408388:0.320546:0.404246:0.320546:0.000000
i.:@0.427981:0.337044:0.434550:0.337044:0.434550:0.320546:0.427981:0.320546:0.000000:0.000000
 :@0.434550:0.337044:0.438693:0.337044:0.438693:0.320546:0.434550:0.320546:0.000000
c|a c|b:@0.438365:0.337160:0.496103:0.337160:0.496103:0.320691:0.438365:0.320691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y :@0.459364:0.337044:0.475142:0.337044:0.475142:0.320546:0.459364:0.320546:0.000000:0.000000:0.000000
.    Si       es un divisor común de   y  , entonces :@0.496103:0.337044:0.868102:0.337044:0.868102:0.320546:0.496103:0.320546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ii.:@0.506487:0.337044:0.516871:0.337044:0.516871:0.320546:0.506487:0.320546:0.000000:0.000000:0.000000
d:@0.536310:0.337160:0.545480:0.337160:0.545480:0.320691:0.536310:0.320691:0.000000
:@0.549329:0.336525:0.563981:0.336525:0.563981:0.323152:0.549329:0.323152:0.000000
Z:@0.567800:0.335957:0.580091:0.335957:0.580091:0.323095:0.567800:0.323095:0.000000
+:@0.580091:0.330691:0.586392:0.330691:0.586392:0.321073:0.580091:0.321073:0.000000
a b:@0.758985:0.337160:0.792680:0.337160:0.792680:0.320691:0.758985:0.320691:0.000000:0.000000:0.000000
d|c:@0.867774:0.337160:0.888966:0.337160:0.888966:0.320691:0.867774:0.320691:0.000000:0.000000:0.000000
.:@0.888966:0.337044:0.891721:0.337044:0.891721:0.320546:0.888966:0.320546:0.000000
Escribiremos  = :@0.427973:0.354395:0.548516:0.354395:0.548516:0.337897:0.427973:0.337897:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c mcd a b:@0.522238:0.354510:0.610647:0.354510:0.610647:0.338042:0.522238:0.338042:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ). :@0.579553:0.354395:0.623497:0.354395:0.623497:0.337897:0.579553:0.337897:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ecuación lineal con dos incógnitas. Soluciones enteras :@0.404236:0.390494:0.840438:0.390494:0.840438:0.372811:0.404236:0.372811:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
no negativas :@0.404236:0.408599:0.509010:0.408599:0.509010:0.390916:0.404236:0.390916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Consideramos ecuaciones lineales con dos incógnitas de la forma:@0.404236:0.425307:0.867215:0.425307:0.867215:0.408809:0.404236:0.408809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ax by c:@0.607253:0.449901:0.686010:0.449901:0.686010:0.433433:0.607253:0.433433:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 +   =  ,:@0.623725:0.449786:0.688765:0.449786:0.688765:0.433288:0.623725:0.433288:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
donde  ,      , tales que | | + | | > 0, y   ,       denotan las incógnitas. :@0.404236:0.481465:0.895893:0.481469:0.895893:0.464971:0.404236:0.464968:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.453093:0.481581:0.476751:0.481581:0.476751:0.465112:0.453093:0.465112:0.000000:0.000000:0.000000
:@0.479654:0.480950:0.494306:0.480950:0.494306:0.467577:0.479654:0.467577:0.000000
R:@0.497222:0.480382:0.510527:0.480382:0.510527:0.467520:0.497222:0.467520:0.000000
a:@0.584591:0.481585:0.593568:0.481585:0.593568:0.465116:0.584591:0.465116:0.000000
b:@0.619732:0.481585:0.628999:0.481585:0.628999:0.465116:0.619732:0.465116:0.000000
x y:@0.678125:0.481585:0.698720:0.481585:0.698720:0.465116:0.678125:0.465116:0.000000:0.000000:0.000000
:@0.701610:0.480950:0.716262:0.480950:0.716262:0.467577:0.701610:0.467577:0.000000
R:@0.719176:0.480382:0.732481:0.480382:0.732481:0.467520:0.719176:0.467520:0.000000
Nos interesamos ahora en la búsqueda de soluciones enteras positivas, :@0.404230:0.513149:0.895949:0.513149:0.895949:0.496651:0.404230:0.496651:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuando  ,       es decir, en hallar  ,      , tales que :@0.404230:0.530499:0.793945:0.530504:0.793945:0.514006:0.404230:0.514002:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.461891:0.530615:0.486801:0.530615:0.486801:0.514146:0.461891:0.514146:0.000000:0.000000:0.000000
:@0.490792:0.529985:0.505445:0.529985:0.505445:0.516612:0.490792:0.516612:0.000000
Z:@0.509440:0.529417:0.521731:0.529417:0.521731:0.516555:0.509440:0.516555:0.000000
m n:@0.648209:0.530619:0.679035:0.530619:0.679035:0.514151:0.648209:0.514151:0.000000:0.000000:0.000000
:@0.683021:0.529985:0.697674:0.529985:0.697674:0.516612:0.683021:0.516612:0.000000
Z:@0.701668:0.529417:0.713960:0.529417:0.713960:0.516555:0.701668:0.516555:0.000000
+:@0.713886:0.524151:0.720187:0.524151:0.720187:0.514533:0.713886:0.514533:0.000000
am bn c:@0.793867:0.530619:0.880659:0.530619:0.880659:0.514151:0.793867:0.514151:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 +   =  .:@0.817334:0.530504:0.883337:0.530504:0.883337:0.514006:0.817334:0.514006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicio resuelto:@0.404249:0.565581:0.522227:0.565581:0.522227:0.548794:0.404249:0.548794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1):@0.404249:0.582773:0.419449:0.582773:0.419449:0.566058:0.404249:0.566058:0.000000:0.000000
  Considerar la ecuación ( ,  )    , tal que 2  + 3  = 10. :@0.419449:0.582556:0.823054:0.582556:0.823054:0.566058:0.419449:0.566058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.599442:0.582672:0.621501:0.582672:0.621501:0.566203:0.599442:0.566203:0.000000:0.000000:0.000000
:@0.631591:0.582037:0.646244:0.582037:0.646244:0.568664:0.631591:0.568664:0.000000
R:@0.650386:0.581469:0.663691:0.581469:0.663691:0.568607:0.650386:0.568607:0.000000
2:@0.663689:0.576203:0.668642:0.576203:0.668642:0.566585:0.663689:0.566585:0.000000
x:@0.737323:0.582672:0.744798:0.582672:0.744798:0.566203:0.737323:0.566203:0.000000
y:@0.772386:0.582672:0.780073:0.582672:0.780073:0.566203:0.772386:0.566203:0.000000
Determinar todas las soluciones enteras de esta ecuación, esto es, :@0.427981:0.599907:0.895331:0.599907:0.895331:0.583409:0.427981:0.583409:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hallar ( ,  )    , tal que 2  + 3  = 10.:@0.427981:0.617257:0.713002:0.617257:0.713002:0.600760:0.427981:0.600760:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m n:@0.476549:0.617373:0.507604:0.617373:0.507604:0.600904:0.476549:0.600904:0.000000:0.000000:0.000000
:@0.517697:0.616739:0.532349:0.616739:0.532349:0.603366:0.517697:0.603366:0.000000
Z:@0.536491:0.616171:0.548783:0.616171:0.548783:0.603308:0.536491:0.603308:0.000000
2:@0.548783:0.610904:0.553736:0.610904:0.553736:0.601286:0.548783:0.601286:0.000000
m:@0.622417:0.617373:0.637213:0.617373:0.637213:0.600904:0.622417:0.600904:0.000000
n:@0.664800:0.617373:0.674163:0.617373:0.674163:0.600904:0.664800:0.600904:0.000000
Supongamos ,      , tales que 2  + 3  = 10. Entonces, :@0.427973:0.648937:0.842037:0.648941:0.842037:0.632444:0.427973:0.632439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m n:@0.525725:0.649053:0.556780:0.649053:0.556780:0.632584:0.525725:0.632584:0.000000:0.000000:0.000000
:@0.560926:0.648423:0.575579:0.648423:0.575579:0.635050:0.560926:0.635050:0.000000
Z:@0.579721:0.647855:0.592012:0.647855:0.592012:0.634992:0.579721:0.634992:0.000000
m:@0.675161:0.649057:0.689957:0.649057:0.689957:0.632588:0.675161:0.632588:0.000000
n:@0.717545:0.649057:0.726907:0.649057:0.726907:0.632588:0.717545:0.632588:0.000000
3  = 10 – 2 . De esta igualdad se deduce que 2(5 –  ) debe ser :@0.427988:0.666292:0.890504:0.666292:0.890504:0.649795:0.427988:0.649795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.436484:0.666408:0.445847:0.666408:0.445847:0.649939:0.436484:0.649939:0.000000
m:@0.509210:0.666408:0.524006:0.666408:0.524006:0.649939:0.509210:0.649939:0.000000
m:@0.801672:0.666408:0.816468:0.666408:0.816468:0.649939:0.801672:0.649939:0.000000
múltiplo de 3. Esto es posible si 5 –   es múltiplo de 3, o sea, :@0.427988:0.683643:0.864126:0.683643:0.864126:0.667145:0.427988:0.667145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.680494:0.683759:0.695289:0.683759:0.695289:0.667290:0.680494:0.667290:0.000000
5 –   = 3  para algún      . Es decir,   = 5 – 3   y, en consecuen-:@0.427988:0.700994:0.889777:0.700994:0.889777:0.684496:0.427988:0.684496:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.455267:0.701109:0.470063:0.701109:0.470063:0.684641:0.455267:0.684641:0.000000
j:@0.497651:0.701109:0.501504:0.701109:0.501504:0.684641:0.497651:0.684641:0.000000
j:@0.584133:0.701109:0.587986:0.701109:0.587986:0.684641:0.584133:0.684641:0.000000
:@0.592118:0.700475:0.606770:0.700475:0.606770:0.687102:0.592118:0.687102:0.000000
Z:@0.610912:0.699907:0.623203:0.699907:0.623203:0.687045:0.610912:0.687045:0.000000
m:@0.690399:0.701109:0.705194:0.701109:0.705194:0.684641:0.690399:0.684641:0.000000
j:@0.760062:0.701109:0.763915:0.701109:0.763915:0.684641:0.760062:0.684641:0.000000
cia, 3  = 2(5 –  ) = 6 , de donde   = 2 . Tenemos así,:@0.427989:0.718344:0.802889:0.718344:0.802889:0.701847:0.427989:0.701847:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.463263:0.718460:0.472626:0.718460:0.472626:0.701991:0.463263:0.701991:0.000000
m:@0.533447:0.718460:0.548242:0.718460:0.548242:0.701991:0.533447:0.701991:0.000000
j:@0.581783:0.718460:0.585636:0.718460:0.585636:0.701991:0.581783:0.701991:0.000000
n:@0.665566:0.718460:0.674929:0.718460:0.674929:0.701991:0.665566:0.701991:0.000000
j:@0.702517:0.718460:0.706370:0.718460:0.706370:0.701991:0.702517:0.701991:0.000000
 :@0.404254:0.750776:0.408396:0.750776:0.408396:0.734278:0.404254:0.734278:0.000000
    = 5 – 3 ,:@0.427989:0.750776:0.512544:0.750776:0.512544:0.734278:0.427989:0.734278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.436273:0.750892:0.451068:0.750892:0.451068:0.734423:0.436273:0.734423:0.000000
j:@0.505936:0.750892:0.509789:0.750892:0.509789:0.734423:0.505936:0.734423:0.000000
 :@0.404254:0.768127:0.408396:0.768127:0.408396:0.751629:0.404254:0.751629:0.000000
    = 2 , :@0.427989:0.768127:0.483973:0.768127:0.483973:0.751629:0.427989:0.751629:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.436273:0.768242:0.445636:0.768242:0.445636:0.751774:0.436273:0.751774:0.000000
j:@0.473223:0.768242:0.477076:0.768242:0.477076:0.751774:0.473223:0.751774:0.000000
j:@0.544967:0.759437:0.548820:0.759437:0.548820:0.742968:0.544967:0.742968:0.000000
   :@0.548820:0.759321:0.571746:0.759332:0.571746:0.742835:0.548820:0.742823:0.000000:0.000000:0.000000
:@0.552951:0.758814:0.567603:0.758814:0.567603:0.745441:0.552951:0.745441:0.000000
Z:@0.571745:0.758246:0.584036:0.758246:0.584036:0.745383:0.571745:0.745383:0.000000
.:@0.584036:0.759448:0.586888:0.759448:0.586888:0.742979:0.584036:0.742979:0.000000
 :@0.404234:0.800569:0.408376:0.800569:0.408376:0.784072:0.404234:0.784072:0.000000
Veamos algunas soluciones enteras::@0.427968:0.800569:0.679781:0.800569:0.679781:0.784072:0.427968:0.784072:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las soluciones enteras están representadas en el conjunto solución::@0.404234:0.899396:0.880658:0.899396:0.880658:0.882899:0.404234:0.882899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.565715:0.923991:0.573595:0.923991:0.573595:0.907522:0.565715:0.907522:0.000000
 = {(5 – 3 , 2 ) |      }.:@0.573595:0.923875:0.730299:0.923874:0.730299:0.907377:0.573595:0.907378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j j j:@0.640272:0.923991:0.686470:0.923991:0.686470:0.907522:0.640272:0.907522:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.690602:0.923356:0.705254:0.923356:0.705254:0.909983:0.690602:0.909983:0.000000
Z:@0.709396:0.922788:0.721687:0.922788:0.721687:0.909925:0.709396:0.909925:0.000000
j:@0.461905:0.828031:0.466124:0.828031:0.466124:0.811245:0.461905:0.811245:0.000000
–1:@0.530134:0.826354:0.547478:0.826354:0.547478:0.811291:0.530134:0.811291:0.000000:0.000000
–2:@0.608480:0.826354:0.625823:0.826354:0.625823:0.811291:0.608480:0.811291:0.000000:0.000000
0:@0.691628:0.826354:0.699385:0.826354:0.699385:0.811291:0.691628:0.811291:0.000000
1:@0.769974:0.826354:0.777731:0.826354:0.777731:0.811291:0.769974:0.811291:0.000000
2:@0.848320:0.826354:0.856077:0.826354:0.856077:0.811291:0.848320:0.811291:0.000000
m:@0.456529:0.846437:0.471498:0.846437:0.471498:0.829650:0.456529:0.829650:0.000000
8:@0.534927:0.845250:0.542684:0.845250:0.542684:0.830187:0.534927:0.830187:0.000000
11:@0.609403:0.845250:0.624917:0.845250:0.624917:0.830187:0.609403:0.830187:0.000000:0.000000
5:@0.691636:0.845250:0.699393:0.845250:0.699393:0.830187:0.691636:0.830187:0.000000
2:@0.769982:0.845250:0.777739:0.845250:0.777739:0.830187:0.769982:0.830187:0.000000
–1:@0.843544:0.845250:0.860887:0.845250:0.860887:0.830187:0.843544:0.830187:0.000000:0.000000
n:@0.459218:0.864843:0.468812:0.864843:0.468812:0.848056:0.459218:0.848056:0.000000
–2:@0.530134:0.863656:0.547478:0.863656:0.547478:0.848593:0.530134:0.848593:0.000000:0.000000
–4:@0.608480:0.863656:0.625823:0.863656:0.625823:0.848593:0.608480:0.848593:0.000000:0.000000
0:@0.691628:0.863656:0.699385:0.863656:0.699385:0.848593:0.691628:0.848593:0.000000
2:@0.769974:0.863656:0.777731:0.863656:0.777731:0.848593:0.769974:0.848593:0.000000
4:@0.848320:0.863656:0.856077:0.863656:0.856077:0.848593:0.848320:0.848593:0.000000
Saberes previos:@0.199646:0.115710:0.307805:0.115710:0.307805:0.100238:0.199646:0.100238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuándo un número es :@0.199884:0.144338:0.355028:0.144338:0.355028:0.129274:0.199884:0.129274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
divisor de otro?:@0.153341:0.160180:0.252955:0.160180:0.252955:0.145116:0.153341:0.145116:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.207331:0.363493:0.207331:0.363493:0.191858:0.199646:0.191858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuáles son los términos :@0.199884:0.235958:0.362273:0.235958:0.362273:0.220895:0.199884:0.220895:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de una división?:@0.153341:0.251800:0.256629:0.251800:0.256629:0.236737:0.153341:0.236737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recuerda que…:@0.199644:0.586073:0.309404:0.586073:0.309404:0.570600:0.199644:0.570600:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.153344:0.629228:0.160433:0.629228:0.160433:0.613531:0.153344:0.613531:0.000000
  Se dice que dos números en-:@0.160433:0.628581:0.357474:0.628581:0.357474:0.613518:0.160433:0.613518:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
teros   y   son primos entre :@0.169966:0.644423:0.354994:0.644423:0.354994:0.629360:0.169966:0.629360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.205815:0.644528:0.237178:0.644528:0.237178:0.629492:0.205815:0.629492:0.000000:0.000000:0.000000
sí, si :@0.169966:0.660265:0.198410:0.660265:0.198410:0.645202:0.169966:0.645202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mcd a b:@0.198410:0.660370:0.255137:0.660370:0.255137:0.645334:0.198410:0.645334:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ) = 1. :@0.226747:0.660265:0.292059:0.660265:0.292059:0.645202:0.226747:0.645202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.153344:0.683882:0.160433:0.683882:0.160433:0.668186:0.153344:0.668186:0.000000
  Sean  ,  ,   :@0.160433:0.683236:0.244332:0.683236:0.244332:0.668172:0.160433:0.668172:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b x:@0.204476:0.683341:0.240552:0.683341:0.240552:0.668305:0.204476:0.668305:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.244333:0.682887:0.262476:0.682887:0.262476:0.670150:0.244333:0.670150:0.000000:0.000000
Z:@0.262476:0.682233:0.273650:0.682233:0.273650:0.670540:0.262476:0.670540:0.000000
 no nulos. :@0.273648:0.683236:0.340805:0.683236:0.340805:0.668172:0.273648:0.668172:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Entonces,:@0.169955:0.699078:0.232046:0.699078:0.232046:0.684014:0.169955:0.684014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.153332:0.714920:0.157114:0.714920:0.157114:0.699856:0.153332:0.699856:0.000000
mcd xa xb:@0.169955:0.715025:0.240403:0.715025:0.240403:0.699988:0.169955:0.699988:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ) =  ∙ :@0.198292:0.714920:0.280174:0.714920:0.280174:0.699856:0.198292:0.699856:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x  mcd a b:@0.263270:0.715025:0.336902:0.715025:0.336902:0.699988:0.263270:0.699988:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ).:@0.308511:0.714920:0.344852:0.714920:0.344852:0.699856:0.308511:0.699856:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
• :@0.153332:0.738537:0.164414:0.738537:0.164414:0.722841:0.153332:0.722841:0.000000:0.000000
El múltiplo común de   y :@0.169955:0.737890:0.338219:0.737890:0.338219:0.722827:0.169955:0.722827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.315317:0.737996:0.323514:0.737996:0.323514:0.722959:0.315317:0.722959:0.000000
b:@0.169955:0.754591:0.178416:0.754591:0.178416:0.739554:0.169955:0.739554:0.000000
 se define como     :@0.178416:0.754485:0.316478:0.754485:0.316478:0.739422:0.178416:0.739422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.285801:0.754591:0.294262:0.754591:0.294262:0.739554:0.285801:0.739554:0.000000
:@0.298044:0.754287:0.312696:0.754287:0.312696:0.740914:0.298044:0.740914:0.000000
Z:@0.316485:0.753719:0.328777:0.753719:0.328777:0.740857:0.316485:0.740857:0.000000
+:@0.328777:0.748686:0.334530:0.748686:0.334530:0.739905:0.328777:0.739905:0.000000
, :@0.334529:0.754486:0.340827:0.754486:0.340827:0.739422:0.334529:0.739422:0.000000:0.000000
tal que :@0.169957:0.770328:0.218611:0.770328:0.218611:0.755264:0.169957:0.755264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a|p b|p:@0.218611:0.770433:0.275726:0.770433:0.275726:0.755396:0.218611:0.755396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y :@0.239684:0.770328:0.254389:0.770328:0.254389:0.755264:0.239684:0.755264:0.000000:0.000000:0.000000
. El mínimo :@0.275726:0.770328:0.352313:0.770328:0.352313:0.755264:0.275726:0.755264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
común múltiplo de   y  , :@0.169957:0.786170:0.338169:0.786170:0.338169:0.771106:0.169957:0.771106:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.300509:0.786275:0.331872:0.786275:0.331872:0.771238:0.300509:0.771238:0.000000:0.000000:0.000000
que se denota :@0.169957:0.802012:0.265893:0.802012:0.265893:0.786948:0.169957:0.786948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mcm a b:@0.265893:0.802117:0.327617:0.802117:0.327617:0.787080:0.265893:0.787080:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  ), se :@0.299226:0.802012:0.356429:0.802012:0.356429:0.786948:0.299226:0.786948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
define como el más pequeño :@0.169957:0.817854:0.363673:0.817854:0.363673:0.802790:0.169957:0.802790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
número entero     :@0.169957:0.834448:0.302445:0.834448:0.302445:0.819385:0.169957:0.819385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.271768:0.834554:0.280229:0.834554:0.280229:0.819517:0.271768:0.819517:0.000000
:@0.284011:0.834250:0.298663:0.834250:0.298663:0.820877:0.284011:0.820877:0.000000
Z:@0.302452:0.833684:0.314743:0.833684:0.314743:0.820821:0.302452:0.820821:0.000000
+:@0.314743:0.827392:0.320496:0.827392:0.320496:0.818610:0.314743:0.818610:0.000000
, tal :@0.320496:0.834450:0.347004:0.834450:0.347004:0.819387:0.320496:0.819387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que :@0.169961:0.850292:0.198404:0.850292:0.198404:0.835229:0.169961:0.835229:0.000000:0.000000:0.000000:0.000000
a|p b|p:@0.198404:0.850398:0.255518:0.850398:0.255518:0.835361:0.198404:0.835361:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y :@0.219477:0.850292:0.234182:0.850292:0.234182:0.835229:0.219477:0.835229:0.000000:0.000000:0.000000
.:@0.255518:0.850292:0.258034:0.850292:0.258034:0.835229:0.255518:0.835229:0.000000
Interdisciplinariedad:@0.199646:0.295613:0.346431:0.295613:0.346431:0.280141:0.199646:0.280141:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Matemática e Historia:@0.199884:0.323370:0.355552:0.323370:0.355552:0.307897:0.199884:0.307897:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El sistema sexagesimal del que :@0.153341:0.338789:0.351541:0.338789:0.351541:0.323726:0.153341:0.323726:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nos valemos para las horas, :@0.153341:0.354631:0.332509:0.354631:0.332509:0.339568:0.153341:0.339568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
minutos o grados, se desarro-:@0.153341:0.370473:0.344294:0.370473:0.344294:0.355410:0.153341:0.355410:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lló hace siglos, en la antigua :@0.153341:0.386315:0.334271:0.386315:0.334271:0.371252:0.153341:0.371252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Babilonia.:@0.153341:0.402157:0.215750:0.402157:0.215750:0.387094:0.153341:0.387094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La geometría tiene origen en el :@0.153341:0.417999:0.356556:0.417999:0.356556:0.402936:0.153341:0.402936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
antiguo Egipto y Babilonia, ya :@0.153341:0.433841:0.347429:0.433841:0.347429:0.418778:0.153341:0.418778:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que necesitaban realizar medi-:@0.153341:0.449683:0.350611:0.449683:0.350611:0.434620:0.153341:0.434620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ciones en la tierra para construir :@0.153341:0.465525:0.364560:0.465525:0.364560:0.450462:0.153341:0.450462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y desarrollar otras ciencias. Los :@0.153341:0.481367:0.354180:0.481367:0.354180:0.466304:0.153341:0.466304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
números negativos se empeza-:@0.153341:0.497209:0.353723:0.497209:0.353723:0.482146:0.153341:0.482146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ron a usar en la India, en el siglo :@0.153341:0.513051:0.361394:0.513051:0.361394:0.497988:0.153341:0.497988:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
VII, para indicar las deudas.:@0.153341:0.528893:0.327654:0.528893:0.327654:0.513830:0.153341:0.513830:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000