Strayer Elementary Number Theory 2. 5. 65a.

Ok so this one obviously sucks. I got completely stuck, not anticipating the proof would rely on the CRT. So thanks to Math Overflow for any progress on this one.

I think everything here is necessary and correct. Sorry if not. I'm over this problem. Using Dirichelet's Thm. for Lemma 2 may not be OK since it wasn't proven in the book, only mentioned. In that case, I bet there's another way to prove Lemma 2. But I don't care to waste any more time on this problem.

Lemma 1:

Lemma 2:

Proof: