Autors: Stoenchev, M. R., V. Todorov.
Title: On the classical diophantine equation x^4 + y^4 + kx^2y^2 = z^2
Keywords: elliptic curves, Mordell-Weil group, diophantine equations

Abstract: The purpose of this article is to describe parametrically all nontrivial solutions of the Diophantine equation in the title. One parameter family of elliptic curves is naturally associated with the equation for which family we apply "complete 2-descend" algorithm to obtain a parametric description of all possible values for the parameter k belongs to Z, for which nontrivial solutions exist.



    , vol. 2333, pp. 11002-1--110002-14, 2021, United States, AIP Publishing,

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