Alright, having problems with this question too. It seems to be the same type of number theory problem, which is the problem. 1. The problem statement, all variables and given/known data Prove "The square of any integer has the form 4k or 4k+1 for some integer k. 2. Relevant equations definition of even= 2k definition of odd= 2k+1 3. The attempt at a solution Basically I have: Case 1. 2k(2k) = 4k Case 2. 2k+1(2k+1) = 4k2+4k+1 = 4k+1(k+1) Not sure if it's correct. Do I need to use different indices? I feel I am missing something. Thanks for any help!