Stupid little question. Just wanted you to check my work. This was the quickest way I saw to do it, but i'm not convinced it's the best way, or even valid at all.

Problem:

Prove that if , then there is a solution (for ) to the congruence .

Solution:

Proof.

Assume . Then for . We want to show that there exists an such that , for (since this would mean

). Rearranging our first equation we have . It suffices to take

QED

does that work?

Thanks guys