On Pythagorean Triples and the Primitive Roots Modulo a Prime

被引：0

作者：

Wang, Jingzhe ^{[1
]}

机构：

[1] Inner Mongolia Univ Finance & Econ, Sch Stat & Math, Hohhot 010070, Inner Mongolia, Peoples R China

来源：

JOURNAL OF MATHEMATICS | 2021年 / 2021卷

关键词：

SUMS;

D O I：

10.1155/2021/7634728

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 x(2)+y(2)=z(2).

引用

页数：8

共 50 条

[1] Pythagorean triples and quadratic residues modulo an odd prime
Hu, Jiayuan
Zhan, Yu
[J]. AIMS MATHEMATICS, 2022, 7 (01): : 957 - 966
[2] On the distribution of primitive roots modulo a prime
Yi, Y
Zhang, WP
[J]. PUBLICATIONES MATHEMATICAE-DEBRECEN, 2002, 61 (3-4): : 383 - 391
[3] PRIMITIVE PYTHAGOREAN TRIPLES WITH SUM OR DIFFERENCE OF LEGS EQUAL TO A PRIME
WEGENER, DP
[J]. FIBONACCI QUARTERLY, 1975, 13 (03): : 263 - 277
[4] PAIRS OF CONSECUTIVE PRIMITIVE ROOTS MODULO A PRIME
VEGH, E
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1968, 19 (05) : 1169 - &
[5] Lehmer numbers and primitive roots modulo a prime
Cohen, Stephen D.
Trudgian, Tim
[J]. JOURNAL OF NUMBER THEORY, 2019, 203 : 68 - 79
[6] PRIMITIVE PYTHAGOREAN TRIPLES
BERNSTEIN, L
[J]. FIBONACCI QUARTERLY, 1982, 20 (03): : 227 - 241
[7] LEAST PRIMITIVE ROOTS MODULO THE SQUARE OF A PRIME IDEAL
HINZ, JG
[J]. MATHEMATIKA, 1986, 33 (66) : 244 - 252
[8] PELL PRIMITIVE PYTHAGOREAN TRIPLES
BRUCKMAN, PS
[J]. FIBONACCI QUARTERLY, 1990, 28 (03): : 279 - 280
[9] PRIMITIVE ROOTS MODULO A PRIME AS CONSECUTIVE TERMS OF AN ARITHMETIC PROGRESSION
VEGH, E
[J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1969, 235 : 185 - &
[10] PRIMITIVE PYTHAGOREAN TRIPLES AND THE INFINITUDE OF PRIMES
WEGENER, DP
[J]. FIBONACCI QUARTERLY, 1981, 19 (05): : 449 - 450

← 1 2 3 4 5 →