A Modular Arithmetic Proof Problem

[e(ho0n3]

Homework Statement
Let a, b, s, t be integers with s, t > 0. What conditions must s, t satisfy if the following statement is true:

If a = b (mod s) and a = b (mod t), then a = b (mod st).

The attempt at a solution
If s | a, s | b, t | a and t | b, then st | a and st | b if and only if s, t are relatively prime. This is as far as I've gone. How should I continue?

 

[Dick]

The statement is equivalent to s | (b-a) and t | (b-a) -> st | (b-a).

 

[e(ho0n3]

Oh, that's right! I completely forgot about that. And by using what I have, I can conclude that s and t must be relatively prime.

Thanks again.