Monday, November 1, 2010

Odd primes and Square numbers

Question:
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For what odd primes p is x = (2^(p - 1) - 1)/p an integer square?

Let be be some odd prime, and x = (2^(p - 1) - 1)/p
For what p is x an integer square, i.e. solve for p :

a^2 = (2^(p - 1) -1)/p
pa^2 = 2^(p - 1) -1

The trivial solutions are: p = 3 and p = 7


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