References & Citations
Mathematics > Number Theory
Title: Asymptotic Fermat's Last Theorem for a family of equations of signature $(2, 2n, n)$
(Submitted on 22 Apr 2024)
Abstract: In this paper, we study the integer solutions of a family of Fermat-type equations of signature $(2, 2n, n)$, $Cx^2 + q^ky^{2n} = z^n$. We provide an algorithmically testable set of conditions which, if satisfied, imply the existence of a constant $B_{C, q}$ such that if $n > B_{C,q}$, 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.
Submission history
From: Pedro-José Cazorla García [view email][v1] Mon, 22 Apr 2024 11:35:09 GMT (28kb)
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