Construction of diagonal quintic threefolds with infinitely many rational points
| Autor: | Ulas, Maciej |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this note we present a construction of an infinite family of diagonal quintic threefolds defined over $\Q$ 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. Comment: 9 pages; accepted for publication in Mathematics of Computation |
| Databáze: | arXiv |
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