AN ELEMENTARY APPROACH TO ((p-1)/4(p-1)/2) modulo p2

被引：4

作者：

Pan, Hao ^{[1
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2012年 / 16卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Binomial coefficient; Legendre symbol;

D O I：

10.11650/twjm/1500406847

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give an elementary proof of the well-known congruence ((p-1/2)(p-1/4)) equivalent to 2(p-1) + 1 /2 (2a - p/2a) (mod p(2)), where p equivalent to 1 (mod 4) is prime and p = a(2) + b(2) with a equivalent to 1 (mod 4).

引用

页码：2197 / 2202

页数：6

共 9 条

[1] On some congruence conjectures modulo p2
Mao, Guo-Shuai
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2022, 101 (1-2): : 33 - 45
[2] On equations (-1/)α px (-1/)β (2k(2p+1))y = z2 with Sophie Germain prime p
Li, Yuan
Zhang, Jing
Liu, Baoxing
INVOLVE, A JOURNAL OF MATHEMATICS, 2024, 17 (03): : 503 - 518
[3] On the Diophantine Equations qx + p(2q + 1)y = z2 and qx
Phosri, Piyada
Tadee, Suton
THAI JOURNAL OF MATHEMATICS, 2024, 22 (02): : 389 - 395
[4] On the Diophantine Equations (p +a)x -py =z2 and px- (p +a)y =z2
Tadee, Suton
Wannaphan, Chantana
INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, 2024, 19 (02) : 459 - 465
[5] On R. Chapman's "evil determinant": case p 1 (mod 4)
Vsemirnov, Maxim
ACTA ARITHMETICA, 2013, 159 (04) : 331 - 344
[6] An explicit expression for all distinct self-dual cyclic codes of length pk over Galois ring GR(p2,m)
Cao, Yuan
Cao, Yonglin
Fu, Fang-Wei
Jitman, Somphong
Mi, Jiafu
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2023, 34 (03) : 489 - 520
[7] UPPER BOUNDS FOR THE NUMBER OF SOLUTIONS FOR THE DIOPHANTINE EQUATION y2 = px(Ax2 - C) (C=2, ±1, ±4)
Bencherif, Farid
Boumahdi, Rachid
Garici, Tarek
Schedler, Zak
COLLOQUIUM MATHEMATICUM, 2020, 159 (02) : 243 - 257
[8] On the Divergence of Two Subseries E 1p, and Theorems of De La Valle acute accent e Poussin and Landau-Walfisz
Reddy, G. Sudhaamsh Mohan
Rau, S. Srinivas
Uma, B.
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2023, 41
[9] An explicit expression for all distinct self-dual cyclic codes of length pk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p^k$$\end{document} over Galois ring GR(p2,m)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{GR}(p^2,m)$$\end{document}
Yuan Cao
Yonglin Cao
Fang-Wei Fu
Somphong Jitman
Jiafu Mi
Applicable Algebra in Engineering, Communication and Computing, 2023, 34 (3) : 489 - 520

← 1 →