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

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 z^n = x^n + y^n 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 z^n - y^n = x^n, and z^n - y^n / A and B, when A = a^n and B = b^n, 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 b integers, and that is not possible.

The authors declare no conflict of interest.

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The datasets used in this study are openly available at [repository link] and the source code is available on GitHub at [GitHub link].

This work did not receive any external funding.