
Re: Decomposition of a 10th degree equation
Posted:
Mar 15, 2013 9:09 AM


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.

