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Asymptotic Fermat's Last Theorem for a family of equations of signature $(2, 2n, n)$
Published 22 Apr 2024 in math.NT | (2404.14098v1)
Abstract: In this paper, we study the integer solutions of a family of Fermat-type equations of signature $(2, 2n, n)$, $Cx2 + qky{2n} = zn$. 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.
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