Posted by lin on Friday, July 5, 2013 at 8:20am.
I suppose this question isn't live anymore. Anyways next time please don't post brilliant problems (:
Well, here's a few hints for you to work out and be on the right track:
Step 1: quadratic reciprocity and CRT
Step 2: incorporate dirichlet's theorem into this.
Well, you can then see obviously that {3,5,6,7,10,11,12,13,14,17,19,20,22,23,24,26,27,28,29,31}. Now just try to prove that the desired answer is minimal. This is simple. Show that 2 and 3 MUST be quadratic residues.
Ok to clarify, the show that 2 and 3 must be quadratic residues part is to find the minimal.