On the number of solutions of some congruences modulo a product of odd prime powers
type: Item
instance of: scholarly article
title: On the number of solutions of some congruences modulo a product of odd prime powers
zbMATH Open document ID: 0177.06702
DOI: 10.1215/S0012-7094-69-03624-2
published in: Duke Mathematical Journal
publication date: 1969-01-01T00:00:00Z
review text: Let \(P_1,P_2,\ldots,P_r\) be distinct odd prime powers and suppose that \(g\) is a primitive root \(\pmod{P_i}\) for each \(i\). Put \(P= \prod_{i=1}^r P_i\) and for each \(i\) put \(f_i = \varphi(P_i)\) and \(f = \text{lcm}_i (f_i)\). Let \(N(g)\) be the number of solutions of the congruence \(g^s + 1 \equiv ^t\pmod P\) with \(0\le s,t< f\). Explicit formulas for \(N(g)\) are obtained in terms of Jacobi sums, thus generalizing work of Carlitz, White, and Whiteman.
Mathematics Subject Classification ID: 11A07
zbMATH DE Number: 3282746
zbMATH Keywords: number of solutions
zbMATH Keywords: congruences modulo a product of odd prime powers
author: David G. Cantor
MaRDI profile type: Publication
full work available at URL: s0012-7094-69-03624-2
OpenAlex ID: W1573597897
description: scientific article