Date: Mar 15, 2013 9:09 AM
Subject: Re: Decomposition of a 10th degree equation
On Mar 15, 7:32 am, Deep <deepk...@yahoo.com> 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.
(A) If (2) and (3) are true, then (1) is true.
This is correct.
But the converse need not be. The converse says:
(B) If (1) is true, then (2) and (3) are true.
And this is an invalid conclusion.