On a problem of Recaman and its generalization
type: Item
instance of: scholarly article
title: On a problem of Recaman and its generalization
zbMATH Open document ID: 1226.11005
author: Lajos Hajdu
author: N. Saradha
published in: Journal of Number Theory
publication date: 2010-11-19T00:00:00Z
full work available at URL: http://hdl.handle.net/2437/110781
review text: Let \(k>1\) be an integer and denote by \(\varphi(k)\) Euler's function. We say that \(k\) is a \(P\)-integer if the first \(\varphi(k)\) primes coprime to \(k\) form a reduced residue system modulo \(k\). The authors prove that the only prime \(P\)-integer is \(2\). Let \(k>1\) be an integer with the least prime divisor \(>\log k\). Then \(k\) is a \(P\)-integer if and only if \(k\in\{2,4,6\}\). Let \(k\) be the product of the primes \(\leq x\) for some \(x\geq 2\). Then \(k\) is a \(P\)-integer if and only if \(k\in\{2,6,30\}\).
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11A07
Mathematics Subject Classification ID: 11A41
zbMATH DE Number: 5817562
zbMATH Keywords: Recaman problem
zbMATH Keywords: Pomerance problem
zbMATH Keywords: Jacobsthal function
zbMATH Keywords: primes in residue classes
MaRDI profile type: Publication
OpenAlex ID: W2031845772
cites work: Computation of Jacobsthal’s function $h(n)$ for $n<50$.
cites work: Q5772619
cites work: A note on the least prime in an arithmetic progression
cites work: Approximate formulas for some functions of prime numbers
cites work: On Jacobsthal's \(g(n)\)-function
DOI: 10.1016/J.JNT.2010.07.002
description: scientific article; zbMATH DE number 5817562