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Sunday, July 18, 2010

Hmmmm....

@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...???

1 comment:

Hemanth said...

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.