Construction of diagonal quintic threefolds with infinitely many rational points
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- by Maciej Ulas;
- Math. Comp. 93 (2024), 2503-2511
- DOI: https://doi.org/10.1090/mcom/3953
- Published electronically: February 14, 2024
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Abstract:
In this note we present a construction of an infinite family of diagonal quintic threefolds defined over $\mathbb {Q}$ each containing infinitely many rational points. As an application, we prove that there are infinitely many quadruples $B=(B_{0}, B_{1}, B_{2}, B_{3})$ of co-prime integers such that for a suitable chosen integer $b$ (depending on $B$), the equation $B_{0}X_{0}^5+B_{1}X_{1}^5+B_{2}X_{2}^5+B_{3}X_{3}^{5}=b$ has infinitely many positive integer solutions.References
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Bibliographic Information
- Maciej Ulas
- Affiliation: Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland
- MR Author ID: 764558
- ORCID: 0000-0002-1927-4453
- Email: maciej.ulas@uj.edu.pl
- Received by editor(s): October 3, 2023
- Received by editor(s) in revised form: November 30, 2023, December 13, 2023, and January 17, 2024
- Published electronically: February 14, 2024
- © Copyright 2024 American Mathematical Society
- Journal: Math. Comp. 93 (2024), 2503-2511
- MSC (2020): Primary 11D41, 13P15
- DOI: https://doi.org/10.1090/mcom/3953
- MathSciNet review: 4759382