Pythagorean triples and quadratic residues modulo an odd prime
| Autor: | Jiayuan Hu, Yu Zhan |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | AIMS Mathematics, Vol 7, Iss 1, Pp 957-966 (2022) |
| Druh dokumentu: | article |
| ISSN: | 2473-6988 |
| DOI: | 10.3934/math.2022057?viewType=HTML |
| Popis: | In this article, we use the elementary methods and the estimate for character sums to study a problem related to quadratic residues and the Pythagorean triples, and prove the following result. Let $ p $ be an odd prime large enough. Then for any positive number $ 0 < \epsilon < 1 $, there must exist three quadratic residues $ x, \ y $ and $ z $ modulo $ p $ with $ 1\leq x, \ y, \ z\leq p^{1+\epsilon} $ such that the equation $ x^2+y^2 = z^2 $. |
| Databáze: | Directory of Open Access Journals |
| Externí odkaz: |
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