Papers › Asymptotic Fermat's Last Theorem for a family of equations of signature (2, 2n, n)
Asymptotic Fermat's Last Theorem for a family of equations of signature (2, 2n, n)
Pedro-José Cazorla García
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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 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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