Math Help - Euclid's Algorithm and Bezout's Identity

1. Euclid's Algorithm and Bezout's Identity

Prove: If $am + bn = e$ for some $e$, then $(a,b)$ divides $e$.

2. Originally Posted by Zennie
Prove: If $am + bn = e$ for some $e$, then $(a,b)$ divides $e$.
By lemma of Euclid Algorithm: if gcd(a,b)= e then there exist m,n (integers) s.t. e= am+bn . Since gcd(a,b) is e. then a divides e. and b divides e?