Question

Daca impartim numerele 2587 si 5172 la abc (abc numar natural) obtinem acelas rest.Cat este abc?

Answer 1

2587:abc= x rest R =>2587=x*abc+R => R=2587-x*abc
5172:abc= y rest R =>5172=y*abc+R => R=5172-y*abc

2587-x*abc=5172-y*abc
y*abc-x*abc=5172-2587
(x-y)*abc=2585

2585=5*11*47

deci, abc =5*47=235
sau abc=47*11=517