On Pythagorean Triples and the Primitive Roots Modulo a Prime
In this paper, we use the elementary methods and the estimates for character sums to study a problem related to primitive roots and the Pythagorean triples and prove the following result: let p be an odd prime large enough. Then, there must exist three primitive roots x, y, and z modulo p such that...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/7634728 |
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| _version_ | 1849405106976456704 |
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| author | Jingzhe Wang |
| author_facet | Jingzhe Wang |
| author_sort | Jingzhe Wang |
| collection | DOAJ |
| description | In this paper, we use the elementary methods and the estimates for character sums to study a problem related to primitive roots and the Pythagorean triples and prove the following result: let p be an odd prime large enough. Then, there must exist three primitive roots x, y, and z modulo p such that x2+y2=z2. |
| format | Article |
| id | doaj-art-4556b5ecc90b4fc6b7c48756e7c04028 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-4556b5ecc90b4fc6b7c48756e7c040282025-08-20T03:36:45ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/76347287634728On Pythagorean Triples and the Primitive Roots Modulo a PrimeJingzhe Wang0School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010070, Inner Mongolia, ChinaIn this paper, we use the elementary methods and the estimates for character sums to study a problem related to primitive roots and the Pythagorean triples and prove the following result: let p be an odd prime large enough. Then, there must exist three primitive roots x, y, and z modulo p such that x2+y2=z2.http://dx.doi.org/10.1155/2021/7634728 |
| spellingShingle | Jingzhe Wang On Pythagorean Triples and the Primitive Roots Modulo a Prime Journal of Mathematics |
| title | On Pythagorean Triples and the Primitive Roots Modulo a Prime |
| title_full | On Pythagorean Triples and the Primitive Roots Modulo a Prime |
| title_fullStr | On Pythagorean Triples and the Primitive Roots Modulo a Prime |
| title_full_unstemmed | On Pythagorean Triples and the Primitive Roots Modulo a Prime |
| title_short | On Pythagorean Triples and the Primitive Roots Modulo a Prime |
| title_sort | on pythagorean triples and the primitive roots modulo a prime |
| url | http://dx.doi.org/10.1155/2021/7634728 |
| work_keys_str_mv | AT jingzhewang onpythagoreantriplesandtheprimitiverootsmoduloaprime |