Abstract
We discuss the rational solutions of the Diophantine equations \(f(x)^2 \pm f(y)^2=z^2\). This problem can be solved either by the theory of elliptic curves or by elementary number theory. Inspired by the work of Ulas and Togbé (Publ Math Debrecen 76(1–2):183–201, 2010) and following the approach of Zhang and Zargar (Period Math Hung, 2018. https://doi.org/10.1007/s10998-018-0259-7) we improve the results concerning the rational solutions of these equations.
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The authors are grateful to the anonymous referee.
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Youmbai, A.E.A., Behloul, D. Rational solutions of the Diophantine equations \(f(x)^2 \pm f(y)^2=z^2\). Period Math Hung 79, 255–260 (2019). https://doi.org/10.1007/s10998-019-00294-1
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DOI: https://doi.org/10.1007/s10998-019-00294-1