Originally Posted by

**lucaswilson94** 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,

Thanks.