Let n be an odd integer not divisible by three. Prove that n^2 is congruent 1 mod 24.
I started by assuming that n is an odd integer divisible by three. So I want to show that n^2 is NOT congruent to 1 mod 24. If n is odd then there exists an integer k such that n=2k+1. so n^2= 4k^2 +4k+1. Now where do I go from here?!