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"