Two theorems on the addition of residue classes
type: Item
instance of: scholarly article
title: Two theorems on the addition of residue classes
zbMATH Open document ID: 0702.11007
DOI: 10.1016/0012-365X(90)90174-G
author: David R. Guichard
published in: Discrete Mathematics
publication date: 1990-01-01T00:00:00Z
review text: It is well known that if \(a_ 1,...,a_ m\) are residues modulo n and \(m\geq n\) then some sum \(a_{i_ 1}+...+a_{i_ k}\), \(i_ 1<...<i_ k\), is 0(mod n). The author generalizes such results and proves three theorems on divisibility properties of subsequences of a finite sequence. Let \(f(a_ 1,...,a_ m;j)\) denote the number of sums formed from the \(a_ i\) which are congruent to j (mod n). Two consequences of these theorems are: (1) If \(f(a_ 1,...,a_ m;0)<2^{m-1}\) then \(f(a_ 1,...,a_ m;0)\leq 3\cdot 2^{m-3}\) and 2) Let \(m\geq 2\). There exist \(a_ 1,...,a_ m\) for which \(f(a_ 1,...,a_ m;j)\) is odd if and only if n is not a power of 2.
Mathematics Subject Classification ID: 11B13
Mathematics Subject Classification ID: 11B83
zbMATH DE Number: 4150261
reviewed by: M. Nair
MaRDI profile type: Publication
cites work: Q3872528
cites work: The addition of residue classes modulo n
full work available at URL: 0012-365x(90)90174-g
OpenAlex ID: W2051850338
description: scientific article; zbMATH DE number 4150261