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- W4310996476 abstract "The purpose of this paper is to show how the modular method together with different techniques can be used to prove non-existence of primitive non-trivial solutions of the equation [Formula: see text] for square-free values [Formula: see text]. The key ingredients are: the approach presented in [A. Pacetti and L. V. Torcomian, [Formula: see text]-curves, Hecke characters and some Diophantine equations, Math. Comp. 91(338) (2022) 2817–2865] (in particular its recipe for the space of modular forms to be computed) together with the use of the symplectic method (as developed in [E. Halberstadt and A. Kraus, Courbes de Fermat: Résultats et problèmes, J. Reine Angew. Math. 548 (2002) 167–234], although we give a variant over ramified extensions needed in our applications) to discard solutions and the use of a second Frey curve, aiming to prove large image of residual Galois representations." @default.
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- W4310996476 date "2023-02-03" @default.
- W4310996476 modified "2023-10-01" @default.
- W4310996476 title "On the equation x2 + dy6 = zp for square-free 1 ≤ d ≤ 20" @default.
- W4310996476 doi "https://doi.org/10.1142/s1793042123500562" @default.
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