Show that if a, b, m and n are integers such that m>0, n>0, n|m and a≡b(mod m) then a≡b(mod n)

You are given:

(1). n|m
(2). a ≡ b (mod m)

From (1), there exists some integer x such that m = xn.
From (2), there exists some integer y such that (a-b) = ym.

Therefore, (a-b) = yxn, and so:

There exists an integer z (equal to yx) such that (a-b) = zn.

Therefore, a ≡ b (mod n).