1. The problem statement, all variables and given/known data prove that if 2 does not divide a then 24 divides a^2-1 2. Relevant equations I know that if 2 does not divide a then a is odd. I proved that the square for all odd integers are of the form 8K+1 I also proved the square of any integer is either in the form 3k, 3k+1 or 3k+2. I know 3k and 3k+2 are even so the odd are in the form 3k+1 3. The attempt at a solution Can I simply say that because both 8 and 3 are in this form then 8*3 is in this form?