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ALGEBRAIC POINTS OF DEGREE AT MOST 2 ON THE AFFINE CURVES $x^p+y^{pq}=1$
Keywords:
Chevalley-Weil theorem, Faltings theorem, Fermat curve, rational pointsAbstract
We determine explicitly the set of algebraic points of degree at most 2 on the affine curves $x^p+y^{pq}=1,$ where $p \in \{5,7,11\}$ and $q$ is a prime number $\geq 5. $
Received: February 25, 2023
Accepted: March 27, 2023
References
B. Gross and D. Rohrlich, Some results on the Mordell-Weil group of the Jacobian of the Fermat curve, Invent. Math. 44 (1978), 201-224.
G. Faltings, Endlichkeitsätze für abelsch Varietäten über Zahlkörpen, Invent. Math. 73 (1983), 349-366.
M. Hindry and J. H. Silverman, Diophantine geometry, an introduction, Graduate Texts in Mathematics 201, Springer-Verlag, 2000.
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