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Topic: ----- ----- ----- conjecture
Replies: 8   Last Post: Jan 2, 2014 6:12 PM

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Posts: 12,067
Registered: 7/15/05
Re: ----- ----- ----- conjecture
Posted: Jan 2, 2014 4:48 PM
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Deep wrote:
>Consider (1) below for the given conditions
>z^p - x^p = 2y^2 (1)
>Conditions: z, x, y are co prime integers taken two at a time,
>2|y, prime p > 3, z > x > y > 0.
>Conjecture: (1) can not be satisfied for the given conditions.
>Any helpful comment upon the correctness of the Conjecture
>will be appreciated.

It's probably correct, but so what?

Here's a more general conjecture ...

Let p be an odd prime and let

f(x,y) = x^p - y^p

restricted t


If f is restricted to

If y,z are coprime positive integers with y < z then the

f(y,z) = y

>Relevant references about the properties of (1) will be very helpful.

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