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.
_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com
________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
