Asymptotic Fermat's last theorem for a family of equations of signature (2,2n,n)$(2, 2n, n)$

Abstract In this paper, we study the integer solutions of a family of Fermat‐type equations of signature , . We provide an algorithmically testable set of conditions which, if satisfied, imply the existence of a constant such that if , there are no solutions of the equation. Our methods use the modular method for Diophantine equations, along with level lowering and Galois theory.

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Publication Details

Journal
Mathematika
Published
2024-08-29
DOI
https://doi.org/10.1112/mtk.12279
Citations
2
Primary Topic
Algebraic Geometry and Number Theory
Type
article
Field-Weighted Citation Impact
2.02
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article

Asymptotic Fermat's last theorem for a family of equations of signature (2,2n,n)$(2, 2n, n)$

Pedro‐José Cazorla García
2 citations
Mathematika
Algebraic Geometry and Number Theory
2.02
article

Asymptotic Fermat's last theorem for a family of equations of signature (2,2n,n)$(2, 2n, n)$

Pedro‐José Cazorla García
article en
2 citations

Abstract

Abstract In this paper, we study the integer solutions of a family of Fermat‐type equations of signature , . We provide an algorithmically testable set of conditions which, if satisfied, imply the existence of a constant such that if , there are no solutions of the equation. Our methods use the modular method for Diophantine equations, along with level lowering and Galois theory.

MathematikaVol. 70(4)
University of Manchester (GB)
Openalex Percentile: Top 14%
Algebraic Geometry and Number Theory
2.02
DOIOpen Access PDFOpenAlex
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Asymptotic Fermat's last theorem for a family of equations of signature (2,2n,n)$(2, 2n, n)$ — Pedro‐José Cazorla García · Mathematika (2024) | TGRS Research Map | TGRS