--- Kris Garrett <[EMAIL PROTECTED]> wrote:
> If it has not been proven that all mersenne numbers
> greater than one is
> prime free then here is a proof for you.
>
> 2^n-1 mod 4 = 3 while n > 1 because every 2^n while
> n > 1 is divisible by 4 itself.
>
> On the other hand every odd square mod 4 is always 1
> because:
>
> if the odd number mod 4 is 1 then:
> n(4)+1 could represent that number
> (4n+1)^2 = 16n^2 + 8n + 1 which mod 4 is 1
>
> if the odd number mod 4 is 3 then:
> n(4)+3 could represent that number
> (4n+3)^2 = 16n^2 + 24n + 9 or 16n^2 + 24n + 4(2) + 1
> which mod 4 is 1
>
> thus the numbers can never be the same above one
> when
> the mersenne number mod 4 is always 3 and the odd
> square mod 4 is
> always 1.
>
Sorry I meant all mersenne numbers square free not prime free.
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