Re: Fermat's Last theorem short proof

In article <wpSdnWHR17REQbrbnZ2dnUVZ_qWvnZ2d@xxxxxxxxxxxx>,
Rick Decker <rdecker@xxxxxxxxxxxx> wrote:

bassam king karzeddin wrote:
Dear All

As a generalization to one of my posts in this thread


Given, two distinct, coprime non zero integers
(x & y),

Theorem- (new or old, I don¹t care), precisely I don't know

If, (n & m) are two positive integers, where

m = gcd ((x+y), n),

then this implies the following theorem:

Gcd ((x+y), (x^n+y^n)/(x+y)) = Rad (m),

Where Rad (m) equals the product of all the prime factors of (m), that is
to say
Rad (m) is square free number that divides (x^n+y^n),

Oh? Perhaps you need another condition, since

x = 15 and y = 49 are coprime and if we pick n = 8 then

m = gcd(x+y, n) = gcd(64, 8) = 8

but 15^8 + 49^8 = (16617746730113)(2) which isn't even
divisible by x+y.

If all you're trying to do is show that (x^n + y^n) / (x + y)
need not be an integer, there are much smaller examples,
e.g., (2^2 + 1^2) / (2 + 1).

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

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