I am working through a past exam as part of my study for uni, and I've come across a question that I can't work out.
Prove or disprove the following statement:
For all intergers n, 3(n^2)-5 is either congruent to 2 modulo 4 or congruent to 3 modulo 4.
I really don't even know where to start with this question, I have rearranged the two modulo terms into 2mod4=4k+2 (for some integer k) and 3mod4=4p+3 (for some integer p), but have no idea whether this is of any help in solving the question or not.
Any help would be greatly appreciated,