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- DevonFangs
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an old one on prime numbers
Show that if p is a prime number > 5, then p^2-1 is a multiple of 24.
an old one on prime numbers
p^2-1=(p+1)*(p-1)The terms on the right side are 2 consecutive even numbers. So one is a multiple of 2 and the other is a multiple of 4. Moreover one of them is also a multiple of 3. (one of 3 consecutive numbers is a multiple of 3 and "p" is prime by definition). So (p^2-1) is a multiple of 2*3*4=24