New reciprocity laws for octic residues and nonresidues

被引：0
|
作者：
Sun, Zhi-Hong [1 ]
机构：
[1] Huaiyin Normal Univ, Sch Math Sci, Huaian 223001, Jiangsu, Peoples R China
来源：
JOURNAL OF NUMBER THEORY | 2015年 / 147卷
基金：
中国国家自然科学基金;
关键词：
Reciprocity law; Octic residue; Congruence; Quartic Jacobi symbol; Lucas sequence; BINARY QUADRATIC-FORMS; QUARTIC CHARACTER; UNITS; PRIMES;
D O I：
10.1016/j.jnt.2014.08.015
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let Z be the set of integers, and let p be a prime of the form 8k + 1. Suppose q is an element of Z, 2 inverted iota q, p inverted iota q, p = c(2) + d(2) = x(2) + 2qy(2), c, d, x, y is an element of Z and c equivalent to 1 (mod 4). In this paper we establish congruences for (-q)((p-1)/8) (mod p) and present new reciprocity laws. (C) 2014 Elsevier Inc. All rights reserved.
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页码：694 / 707
页数：14
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