```Date: Mar 15, 2013 10:20 AM
Author: Deep Deb
Subject: Re: Decomposition of a 10th degree equation

On Friday, March 15, 2013 7:32:06 AM UTC-4, Deep wrote:> Consider the following equation (1) for the given conditions.> > > > x^10 + y^10 = z^10                  (1)> > > > Conditions: x, z are odd integers > 0 and y is non integer but x^10, y^10, z^10 are all integers each > 0> > > > (1) can be decomposed as (2) and (3) where x = uv and u, v are co prime integers.> > > > z^5 + y^5 = u^10           (2)                z^5 - y^5 = v^10          (3)> > > > It is seen that if (2) and (3) are multiplied (1) is obtained.> > > > Question: Is the  decomposition of (1) into (2) and (3) valid?> > > > If not why not.> > Any helpful comment will be appreciated.***   ***   ***KIndly clarify. The solutions of (2) and (3) are also the solutions of (1).  Given, none of (1), (2), (3) has integer solutions. That is y is a non integer in all of them. KIndly clarify the meanings of "valid), "invalid"Thanks again.***   ***   ***
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