ON THE LARGEST PRIME FACTOR OF THE MERSENNE NUMBERS

Abstract

Abstract Let P ( k ) be the largest prime factor of the positive integer k . In this paper, we prove that the series is convergent for each constant α <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].