1. The problem statement, all variables and given/known data Prove that for any integer n n^2+n+1, can never be a square number. 2. Relevant equations None. 3. The attempt at a solution We could put the equation to a^2, (where a^2 is a square number) and solve for n and show that n can not be an integer. I tried quadratic formula on the equation but the solution gets too messy, and i cant prove that the answer is not an integer. There must be an easier way to solve this. Just point me in the right direction.