Asymptotic Fermat's Last Theorem for a family of equations of signature (2, 2n, n)

Pedro-José Cazorla García

Research output: Working paperPreprint

9 Downloads (Pure)

Abstract

In this paper, we study the integer solutions of a family of Fermat-type equations of signature (2, 2n, n), Cx2 + qky2n = zn. We provide an algorithmically testable set of conditions which, if satisfied, imply the existence of a constant BC, q such that if n > BC, q, there are no solutions (x, y, z, n) of the equation. Our methods use the modular method for Diophantine equations, along with level lowering and Galois theory.
Original languageEnglish
Publication statusPublished - 22 Apr 2024

Keywords

  • Exponential Diophantine equation
  • Fermat equations
  • Galois representations
  • Frey-Hellegouarch curve
  • asymptotic Fermat's Last Theorem
  • modularity
  • level lowering

Fingerprint

Dive into the research topics of 'Asymptotic Fermat's Last Theorem for a family of equations of signature (2, 2n, n)'. Together they form a unique fingerprint.

Cite this