Abstract
We consider the diophantine equation \(x^4+y^4+kx^2y^2=z^2\), where \(k\in {\mathbb Z}\) is a parameter. Our aim is to determine for which integers k the equation has a solution in positive integers (x, y, z) and to describe parametrically all nontrivial solutions.
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Acknowledgements
The work is supported by the Bulgarian National Science Fund under Young Scientists Project KP-06-M32/2-17.12.2019 “Advanced Stochastic and Deterministic Approaches for Large-Scale Problems of Computational Mathematics”. Venelin Todorov is supported by the National Scientific Program “Information and Communication Technologies for a Single Digital Market in Science, Education and Security (ICT in SES)", contract No DO1-205/23.11.2018, financed by the Ministry of Education and Science in Bulgaria and by the Bulgarian National Science Fund under Project DN 12/5-2017.
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Apostolov, S., Stoenchev, M., Todorov, V. (2021). One Parameter Family of Elliptic Curves and the Equation \(x^4+y^4+kx^2y^2=z^2\). In: Georgiev, I., Kostadinov, H., Lilkova, E. (eds) Advanced Computing in Industrial Mathematics. BGSIAM 2018. Studies in Computational Intelligence, vol 961. Springer, Cham. https://doi.org/10.1007/978-3-030-71616-5_4
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DOI: https://doi.org/10.1007/978-3-030-71616-5_4
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