proove that if a prime number is represented by this phormula p=(2^n)+1 with n>0 then n is a power of 2... it's all for you...

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- October 22nd 2006, 09:10 AMAglaiafermat...or not fermat?
proove that if a prime number is represented by this phormula p=(2^n)+1 with n>0 then n is a power of 2... it's all for you...

- October 22nd 2006, 09:16 AMThePerfectHacker
The important fact is that, we can factor:

where is odd.

Now, assume,

is prime where is divisible by odd.

Then,

Thus,

Can be factored as,

It has a proper nontrivial factorization, thus it cannot be prime.

Thus, cannot be divisble by odd number that is,

Thus,

Which were studied by Fermat (my favorite mathemation).