Article
Version 7
This version is not peer-reviewed
A Note on Fermat’s Last Theorem
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)
Version 7 : Received: 12 August 2024 / Approved: 12 August 2024 / Online: 13 August 2024 (07:51:25 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)
Version 7 : Received: 12 August 2024 / Approved: 12 August 2024 / Online: 13 August 2024 (07:51:25 CEST)
How to cite: Vega, F. A Note on Fermat’s Last Theorem. Preprints 2021, 2021090480. https://doi.org/10.20944/preprints202109.0480.v7 Vega, F. A Note on Fermat’s Last Theorem. Preprints 2021, 2021090480. https://doi.org/10.20944/preprints202109.0480.v7
Abstract
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.
Keywords
Fermat's Equation; Prime Numbers; Coprime Numbers
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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