I have to prove that if Show that iff I've tried proving the forward direction and im stuck. Here is what I have so far.

proof: : Assume . Assume further that . Let which implies that

Case 1: Suppose . Since and since then d is a common multiple of thus A contradiction.

Case 2: Suppose . Same here as case 1 and d=1. A contradiction.

Case 3: Suppose Since , then A contradiction.\

Would this be right?