A heuristic solution to Fermat's last theorem

Abstract

For centuries, notable mathematicians spent time to prove or refute Fermat's last theorem. As a result, many mathematical proofs have been generated for different values of n. The English mathematician Andrew Wiles, after many attempts, and with the help of his former student Richard Taylor, finally came up with a proof of Fermat's last theorem, which was published in 1995 in the prestigious journal Annals of Mathematics. Because centuries had passed without a proof of the theorem, many mathematicians suspected that Fermat had not developed a real proof. The demonstration presented by Andrew Wiles involved very complex mathematical operations that didn’t exist in Fermat's time. Due to the high complexity of the demonstration of Fermat's last theorem, it is highly challenging to try to find solutions where it is mathematically valid. Therefore, and within this context, this paper aimed to present a heuristic solution of Fermat's last theorem using a specifically developed algebraic method. The purpose was not, under any circumstances, to propose a demonstration of the theorem, but to perform mathematical operations that aimed to facilitate its understanding, and consequently, its application. The outcomes obtained showed that it was possible to obtain valid solutions. This serves as a motivating element for teaching mathematics in undergraduate and even high school.

DOI:  https://doi.org/10.5281/zenodo.7702972