Partitions into two Lehmer numbers
type: Item
instance of: scholarly article
title: Partitions into two Lehmer numbers
zbMATH Open document ID: 1223.11119
author: Igor E. Shparlinski
author: Arne Winterhof
published in: Monatshefte für Mathematik
publication date: 2010-08-06T00:00:00Z
review text: Let \(c,n,q\) be integers with \(q>n\geq 2\) and \(\gcd(cn,q)=1\). For every positive integer \(a\) with \(\gcd(a,q)=1\) denote by \(\text{inv}_{c,q}(a)\) the unique integer \(1\leq\text{inv}_{c,q}(a)<q\) satisfying \(\text{inv}_{c,q}(a)\equiv ca^{-1}(\bmod q)\). The elements of the set \[ {\mathcal L}_{n,c}(q)=\{a\geq 1:\gcd(a,q)=1,n\not\mid a+\text{inv}_{c,q}(a)\} \] are called \((c,n,q)\)-Lehmer numbers. The authors prove an asymptotic formula for the number of representations of an integer as sum of two Lehmer numbers which implies that under some natural restrictions each sufficiently large integer is a sum of two such numbers.
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11N69
Mathematics Subject Classification ID: 11L05
zbMATH DE Number: 5764648
zbMATH Keywords: Lehmer numbers
zbMATH Keywords: exponential sums
zbMATH Keywords: partitions
zbMATH Keywords: Kloosterman sums
MaRDI profile type: Publication
full work available at URL: s00605-009-0130-2
OpenAlex ID: W2021426696
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DOI: 10.1007/S00605-009-0130-2
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description: scientific article; zbMATH DE number 5764648