New reciprocity laws for octic residues and nonresidues

JOURNAL OF NUMBER THEORY

卷:147

Article

Sun, Zhi-Hong

关键词: Reciprocity law;    Octic residue;    Congruence;    Quartic Jacobi symbol;    Lucas sequence;   

DOI  :  10.1016/j.jnt.2014.08.015

来源: Elsevier

【 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.

【 授权许可】

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