Question

Determinati numerele naturale a si b daca (a,b)=18 si a+b=162

Answer 1

(a,b)=18 si a+b=162
(a,b)=1: a=18·m; b=18·n;   (m,n)=1
a+b=18·m+8·n
18(m+n)=162  |:18
m+n=9
(m,n)={(1,8),(2,7),(4,5),(5,4),(7,2),(8,1)}
a=18·m si b=18·n
=> (a,b)={(18,144),(36,126),(72,90),(90,72),(126,36),(144,18)}