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 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
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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. |
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ISSN: | 0253-4142 0973-7685 |
DOI: | 10.1007/s12044-021-00621-y |