On the addition of squares of units modulo n

JOURNAL OF NUMBER THEORY

卷:170

Article

Mollahajiaghaei, Mohsen¹ 

[1] Univ Western Ontario, Dept Math, London, ON N6A 5B7, Canada

关键词: Ring of residue classes;    Squares of units;    Adjacency matrix;    Walks;    Paley graph;   

DOI  :  10.1016/j.jnt.2016.06.013

来源: Elsevier

【 摘 要 】

Let Z(n) be the ring of residue classes modulo n, and let Z(n)* be the group of its units. 90 years ago, Brauer obtained a formula for the number of representations of c is an element of Z(n) as the sum of k units. Recently, Yang and Tang (2015) [6] gave a formula for the number of solutions of the equation x(1)(2) + x(1)(2) = c with x(1), x(2) is an element of Z(n)*,. In this paper, we generalize this result. We find an explicit formula for the number of solutions of the equation x(1)(2) + ... + x(k)(2) = c with x(1),.... x(k) is an element of Z(n)*. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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