@standupmaths on Twitter recently tweeted the following:
"Why is every prime squared (p > 3) always one more than a multiple of 24? [ 5x5-1=24,7x7-1=48...]"
I think I've seen this demonstrated true for all Mersenne primes, but am less clear if it is proven (or even provable) for ALL primes? Can anyone confirm...???
Yes its provable for all primes > 3. You can show that p^2-1 is divisible by 3 as well as 8 separately. Since they are co-prime. p^2-1 is divisible by 24.
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