Patterns of power residues
type: Item
instance of: scholarly article
title: Patterns of power residues
zbMATH Open document ID: 0522.10001
DOI: 10.1016/0022-314X(83)90004-5
published in: Journal of Number Theory
publication date: 1983-01-01T00:00:00Z
review text: Let \(S\) be the set consisting of the \(m\) integers \(0<a_1<\ldots <a_{n-1}\). For any sufficiently large prime \(p\) let \(\Lambda(p)\) denote the least positive \(x\) for which \(x+S\) consists only of \(k\)th power residues modulo \(p\). The author presents evaluations or estimations of \(\limsup_{p\to\infty} \Lambda(p)\) for a number of choices of \(S\) and \(k\).
reviewed by: D. R. B. Burgess
Mathematics Subject Classification ID: 11A15
zbMATH DE Number: 3825907
zbMATH Keywords: higher power residues
zbMATH Keywords: evaluations
zbMATH Keywords: estimations
author: E. T. Lehmer
MaRDI profile type: Publication
cites work: Bounds for Pairs of Consecutive Seventh and Higher Power Residues
cites work: Bounds for Pairs of Cubic Residues
cites work: On Quadruples of Consecutive kth Power Residues
cites work: Unsolved problems in number theory
cites work: On a conjecture of Emma Lehmer
cites work: Totally multiplicative sequences with values±1 which exclude four consecutive values of 1.
cites work: On Runs of Residues
cites work: Pairs of Consecutive Power Residues
cites work: Machine Proof of a Theorem on Cubic Residues
cites work: Integer Sequence having Prescribed Quadratic Character
cites work: On the Bound for a Pair of Consecutive Quartic Residues of a Prime
cites work: Q5514666
cites work: Q5183564
cites work: A recurrent pattern in the list of quadratic residues mod a prime and in the values of the Liouville \(\lambda\) function
description: scientific article; zbMATH DE number 3825907