Construction of diagonal quintic threefolds with infinitely many rational points.
| Autor: | Ulas, Maciej |
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| Zdroj: | Mathematics of Computation; Sep2024, Vol. 93 Issue 349, p2503-2511, 9p |
| Abstrakt: | 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. [ABSTRACT FROM AUTHOR] |
| Databáze: | Complementary Index |
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