Parity Properties of Equations, Related to Fermat Last Theorem

A possibility of elementary proof of Fermat Last Theorem (FLT) on the basis of parity considerations is considered. FLT was formulated by Fermat in 1637, and proved by A. Wiles in 1995. Here, a simpler approach is considered. The idea is to subdivide the initial equation x^n + y^n = z^n into several equations. Then, each one is considered separately, using methods suitable for a particular equation. Proving FLT means to prove that each such sub-equation has no solution in natural numbers. Once this is accomplished, it would mean that the original FLT equation also has no solution in natural numbers.