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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Hindawi Limited
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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doaj-4556b5ecc90b4fc6b7c48756e7c040282021-08-09T00:00:34ZengHindawi LimitedJournal of Mathematics2314-47852021-01-01202110.1155/2021/7634728On Pythagorean Triples and the Primitive Roots Modulo a PrimeJingzhe Wang0School of Statistics and MathematicsIn 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Jingzhe Wang |
| spellingShingle |
Jingzhe Wang On Pythagorean Triples and the Primitive Roots Modulo a Prime Journal of Mathematics |
| author_facet |
Jingzhe Wang |
| author_sort |
Jingzhe Wang |
| title |
On Pythagorean Triples and the Primitive Roots Modulo a Prime |
| title_short |
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_sort |
on pythagorean triples and the primitive roots modulo a prime |
| publisher |
Hindawi Limited |
| series |
Journal of Mathematics |
| issn |
2314-4785 |
| publishDate |
2021-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/2021/7634728 |
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AT jingzhewang onpythagoreantriplesandtheprimitiverootsmoduloaprime |
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