A Note on Fermat’s Last Theorem

Frank Vega

doi:10.20944/preprints202109.0480.v5

Preprint Article Version 5 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 27 September 2021 / Approved: 29 September 2021 / Online: 29 September 2021 (08:30:39 CEST)
Version 2 : Received: 11 October 2021 / Approved: 11 October 2021 / Online: 11 October 2021 (15:38:28 CEST)
Version 3 : Received: 12 October 2021 / Approved: 12 October 2021 / Online: 12 October 2021 (14:31:46 CEST)
Version 4 : Received: 14 October 2021 / Approved: 15 October 2021 / Online: 15 October 2021 (11:14:58 CEST)
Version 5 : Received: 22 July 2024 / Approved: 22 July 2024 / Online: 23 July 2024 (07:33:25 CEST)
Version 6 : Received: 23 July 2024 / Approved: 23 July 2024 / Online: 23 July 2024 (13:53:56 CEST)

Around $1637$, Pierre de Fermat famously scribbled, and claimed to have a proof for, his statement that equation $a^{n} + b^{n} = c^{n}$ has no positive integer solutions for exponents $n>2$. The theorem stood unproven for centuries until Andrew Wiles' groundbreaking work in $1994$, with a notable caveat: Wiles' proof, while successful, relied on modern tools far beyond Fermat's claimed approach in terms of complexity. The present work potentially offers a solution which is closer in spirit to Fermat's original idea.

Fermat's Equation; Prime Numbers; Coprime Numbers

Computer Science and Mathematics, Algebra and Number Theory

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A Note on Fermat’s Last Theorem

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