1. The problem statement, all variables and given/known data If p and q are both greater than or equal to 5, prove that 24|p^2 - q^2 2. Relevant equations none 3. The attempt at a solution 24 = 2^3 * 3. If p = q = 5, then 24|0. If p = 7, q = 5, then 24|24. Any other combination, p^2 - q^2 will be greater than 24. I want to show that p^2 - q^2 will always have a prime factor of either two or three, hence it will be divisible by 24. If p and q are both odd, p^2 - q^2 will always be even, hence have a two in it's prime factorization. A similar situation occurs when p and q are both even. However, when p is odd and q is even, p^2 - q^2 is odd. I want to show that in this case, p^2 - q^2 has a three in it's prime factorization. I checked a few examples on wolfram and they all worked out, can't think of a way to prove this though. Anyone have any gentle guidance :D?