Rational points of the symmetric diagonal equations

In this paper, we consider the symmetric diagonal Diophantine equation x 5 + k y q + k ′ z r = u 5 + k v q + k ′ w r , where k and k ′ are nonzero rational numbers. We prove that if 2 ≤ q , r ≤ 5 and ( q , r ) ≠ ( 5 , 5 ) this equation admits infinitely many nontrivial rational solutions....

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Veröffentlicht in:Proceedings of the Indian Academy of Sciences. Mathematical sciences 2021-10, Vol.131 (2), Article 24
Hauptverfasser: Jalali, A, Janfada, A S, Shabani-Solt, H
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Sprache:eng
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Zusammenfassung:In this paper, we consider the symmetric diagonal Diophantine equation x 5 + k y q + k ′ z r = u 5 + k v q + k ′ w r , where k and k ′ are nonzero rational numbers. We prove that if 2 ≤ q , r ≤ 5 and ( q , r ) ≠ ( 5 , 5 ) this equation admits infinitely many nontrivial rational solutions.
ISSN:0253-4142
0973-7685
DOI:10.1007/s12044-021-00621-y