On the largest prime factor of the mersenne numbers

Kevin Ford, Florian Luca, Igor E. Shparlinski

Research output: Contribution to journalArticle

7 Citations (Scopus)
14 Downloads (Pure)

Abstract

Let P(k) be the largest prime factor of the positive integer k. In this paper, we prove that the series ∑n≥1 (log n)α /{P(2 n-1) is convergent for each constant <1/2, which gives a more precise form of a result of C. L.Stewart [On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers, Proc. London Math. Soc. 35(3) (1977), 425-447].

Original languageEnglish
Pages (from-to)455-463
Number of pages9
JournalBulletin of the Australian Mathematical Society
Volume79
Issue number3
DOIs
Publication statusPublished - Jun 2009

Bibliographical note

Copyright 2009 Cambridge University Press. Article originally published in Bulletin of the Australian Mathematical Society, Vol. 79 No. 3, pp 455-463. The original article can be found at http://dx.doi.org/10.1017/S0004972709000033

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