Question

Determinați perechile de numere naturale nenule (a,b)pentru care: (a,b)=15 si axb=3150

Answer 1

(a;b)=15
a=15 x m
b=15 x n, (m;n)=1
a x b =225 x m x n = 3150
m x n= 14
D14 =1;2;7;14
m=1, n=14 ⇒a=15, b=210
m=14, n=1 ⇒a=210, b=15
m=2, n=7 ⇒a=30, n=105
m=7, n=2 ⇒a=105, b=30
a;b =15;210,  210;15,  30;105,  105;30