TY - JOUR

T1 - On the largest prime factor of the mersenne numbers

AU - Ford, Kevin

AU - Luca, Florian

AU - Shparlinski, Igor E.

N1 - 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

PY - 2009/6

Y1 - 2009/6

N2 - 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].

AB - 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].

UR - http://www.scopus.com/inward/record.url?scp=77957225012&partnerID=8YFLogxK

U2 - 10.1017/S0004972709000033

DO - 10.1017/S0004972709000033

M3 - Article

VL - 79

SP - 455

EP - 463

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

SN - 0004-9727

IS - 3

ER -