Question

show that if a, b, and c are integers with c>0 such that a = b(modc), then (a, c) = (b, c).

Answer 1

Hm. Does (a, c) mean something in particular?

Answer 2

I assume it is an ordered pair and that the = is really a congruence relation modulo m, but clarification would probably be best.

Answer 3

(a, c) = the GCD

Answer 4

That makes a bit more sense, otherwise it would trivially follow :)

Answer 5

And the '=' in a=b(mod c) is a congruence.