On a class of primality criteria
type: Item
instance of: scholarly article
title: On a class of primality criteria
zbMATH Open document ID: 0844.11005
DOI: 10.1007/BF02110568
published in: Mathematical Notes
publication date: 1996-09-01T00:00:00Z
review text: Let \(\binom nk_s\) denote the generalized binomial coefficients defined by \((1+x+ \dots+ x^{s-1})^n= \sum_{k=0}^{n (s-1)} \binom nk_s x^k\), where \(s\geq 2\) is a fixed integer. Generalizing the primality criterion of \textit{H. B. Mann} and \textit{D. Shanks} [J. Comb. Theory, Ser. A 13, 131-134 (1972; Zbl 0239.10010)]\ the author proves that the number \(m\) \((m>1)\) is prime if and only if \(n\mid \binom n{m-2n}_s\) for every \(n\) with \(m/ (s+1)\leq n\leq m/2\).
reviewed by: László Tóth
Mathematics Subject Classification ID: 11A51
Mathematics Subject Classification ID: 11B65
zbMATH DE Number: 830699
zbMATH Keywords: primality criteria
zbMATH Keywords: generalized binomial coefficients
author: Maxim Vsemirnov
MaRDI profile type: Publication
cites work: A necessary and sufficient condition for primality, and its source
cites work: Q3344046
cites work: Q5663959
cites work: Q4405240
full work available at URL: https://doi.org/10.1007/bf02110568
OpenAlex ID: W2093060150
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description: scientific article; zbMATH DE number 830699