# Clue to Puzzle #15: Prime Squared Minus 1 Multiple of 24

15. Why is it that if 'p' is a prime number bigger than 3, then p

^{2}-1 is always divisible by 24 with no remainder?Firstly we need to expand p

^{2}- 1. If you don't know how to do that showing you how to do that may well be enough.

p^{2} - 1 = (p - 1) x (p + 1)

2, 3, 5 are, in the example above, the prime factors of 30.

All prime numbers are, by definition, odd.

Where next?

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