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 language | English (US) |
|---|---|
| Pages (from-to) | 455-463 |
| Number of pages | 9 |
| Journal | Bulletin of the Australian Mathematical Society |
| Volume | 79 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jun 2009 |
Keywords
- Mersenne numbers
- applications of sieve methods
- primes
ASJC Scopus subject areas
- General Mathematics