Choose a prime number greater than 3.
Multiply it by itself and add 14.
Divide by 12 and write down the remainder.
It will always be 3.

WHY?

Another slightly different way of seeing this:
All primes, "p", above 3 are odd, and none are divisible by 3
p^2 - 1 = (p+1)*(p-1) of these factors, one must be divisible by 3 and both must be divisible by 2, so (p^2 - 1) is a multiple of:
3*2*2 = 12, so mod(p^2,12)=1 for all such primes

Posted by Larry on 2010-10-02 00:18:37