On the convergence of series of reciprocals of primes related to the Fermat numbers

JOURNAL OF NUMBER THEORY

卷:97

Article

Krízek, M ; Luca, F ; Somer, L

关键词: Fermat numbers;    elite primes;    sum of reciprocals;    density;   

DOI  :  10.1006/jnth.2002.2782

来源: Elsevier

【 摘 要 】

We examine densities of several sets connected with the Fermat numbers F(m) = 2(2m) + 1. In particular, we prove that the series of reciprocals of all prime divisors of Fermat numbers is convergent. We also show that the series of reciprocals of elite primes is convergent. (C) 2002 Elsevier Science (USA).

【 授权许可】

Free