Proof question

[redfalcon]

Ok, I need help with this proof because I have gotten nowhere with it. Thanks!

Suppose b, m and n are positive integers. If m == n (mod b), prove that gcd(b,m) = gcd(b,n).

[HallsofIvy]

m== n (mod b) means that m= ab+ c, n= db+ c for some integers a, c, d.
From the first equation, c= m- ab so any number that divides both m and b (in particular their gcd) must divide c. Same for any number that divides both m and b.