On the generating functions of Mersenne and Fermat primes
type: Item
instance of: scholarly article
title: On the generating functions of Mersenne and Fermat primes
zbMATH Open document ID: 1270.11004
author: Pablo A. Panzone
published in: Collectanea Mathematica
publication date: 2012-12-04T00:00:00Z
full work available at URL: http://hdl.handle.net/11336/15455
review text: Let \(\mathbf{M}\) and \(\mathbf{F}\) denote the sets of Mersenne and Fermat primes, respectively. Assume that \(\nu(d)\) is an arbitrary completely additive function with \(\nu(d)\ll d^k\) for some \(k>0\). In the paper under review, the author applies a generalization of the so called Golomb's formula to obtain expressions including the summations \(\sum_{p\in\mathbf{M}}\nu(p)z^{2p+1}\) and \(\sum_{p\in\mathbf{F}}\nu(p)z^{2p-1}\). As an application, the author formulates a limit relation, in which under assumption that it is not true, then the set \(\mathbf{M}\cup\mathbf{F}\) is infinite.
reviewed by: Mehdi Hassani
Mathematics Subject Classification ID: 11A41
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 6112442
zbMATH Keywords: Mersenne prime
zbMATH Keywords: Fermat prime
MaRDI profile type: Publication
OpenAlex ID: W1971131074
cites work: Q3751634
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DOI: 10.1007/S13348-010-0019-3
description: scientific article; zbMATH DE number 6112442