Hello, I have a problem with algebra and divisibility etc. I have a swedish textbook that really sucks. Not a good solutions section and no separate solutions manual either. Just a lot of proofs to show. At the moment I'm stuck at proofs with divisibility. I have two examples: 1) Prove that if p is a prime number ≥ 3, then 24 | (p^2 - 1) 2) Prove that if p is a prime number ≥ 3, then 3 | (2p^2 + 1) How to think and show this. I know that p can be written as 2k + 1 since all prime numbers larger than 3 are odd numbers. So in case 1) we have to show that 24 | 4k(k + 1) = 4(k^2 + k). But how? In case 2) we have to show that 3 | 8k^2 + 8k + 3 = 2(4k^2 + 4k) + 3 so we have to show that 3 is divisible by every other odd number? (This is due to the fact that 2(4k^2 + 4k) is an even number and if we add 3 we get the second odd number after... Again, how to show that the number is always divisible by 3... In general I'm having trouble with these type of questions... Hope some of you guys can help me develop my way of thinking... Thanks so very much in advance!