Fermat’s Last Theorem Revisited: Finding a Simple Proof for FLT using the Two Factors, One Even, the other Odd of $z^{n} – y^{n}$ with $z$ and $y$ Odd Numbers

Source abstract

A model for describing and discovering a mathematical solution to a difficult conjecture: the case of Fermat’s last theorem. This implies observation, data analysis, heuristics, intuition, and sometimes serendipity. We shall provide some ideas into finding a solution to the last theorem. The important thing is not only to follow known methods of proof but also to see the problem in a different light, and look in many directions. We shall endeavour to suggest a simple proof for the case of n = 3. Femat’s Last Theorem (FLT) stipulates correctly that there is no integer solution for zⁿ = xⁿ + yⁿ when n > 2, in terms of z, x, and y whole numbers. The main search has been to find a counterexample or prove that there is none, so if zⁿ − yⁿ = xⁿ, and zⁿ − yⁿ / A and B, when A = aⁿ and B = bⁿ, we can make A = 2ⁿ , divide the equation and find B, and show that when a is an integer, b cannot be an integer, but rather an irrational number, however for x to be an integer, a and b must be integers, and that is not possible. Moreover we have also found a way of showing that x is irrational.