1. The problem statement, all variables and given/known data Prove that the product of four consecutive integers is always one less than a perfect square. 3. The attempt at a solution I tried looking at the product [itex] (n-1)(n)(n+1)(n+2)=x^2-1 [/itex] but i couldn't seem to get anything useful out of it. I added one to both sides . I tried to see if i could some how show that the product of the four integers plus 1 had an odd number of divisors but I couldn't see a way to do it. I did notice that these numbers are never divisible by 2,3,or 4, and alot of the time they produce a prime, all though I didn't check very many. And when it wasn't a prime it was divisible by 5. I was trying to think of a way to do this with Pythagorean triples but im not sure.