A Note on Fermat’s Last Theorem

Around 1637, Pierre de Fermat famously wrote in the margin of a book that he had a proof for the equation $a^n + b^n = c^n$ having no positive integer solutions for exponents $n$ greater than 2. This statement, now known as Fermat's Last Theorem, remained unproven for centuries, despite the efforts of countless mathematicians. Andrew Wiles' work in 1994 finally provided a rigorous proof of Fermat's Last Theorem. However, Wiles' proof relied on advanced mathematical techniques that were far beyond the scope of Fermat's time, raising questions about whether Fermat could have truly possessed a proof using the methods available to him. Wiles's achievement was widely celebrated, and he was awarded the Abel Prize in 2016 in recognition of his groundbreaking work. The citation for the award described his proof as a "stunning advance" in mathematics. The present work offers a potential solution to Fermat's Last Theorem that may be more aligned with the original approach that Fermat claimed to have used.