Prime divisors of the Bernoulli and Euler numbers. (English) Zbl 1050.11021
Bennett, M. A. (ed.) et al., Number theory for the millennium III. Proceedings of the millennial conference on number theory, Urbana-Champaign, IL, USA, May 21–26, 2000. Natick, MA: A K Peters (ISBN 1-56881-152-7/hbk). 357-374 (2002).
The Bernoulli numbers may be defined by
It is known that (i) for all ; (ii) the Bernoulli numbers are rational, that is, where for all ; (iii) prime .
The Euler numbers may be defined by
Prime factors of the Euler numbers, and of the numerators of the Bernoulli numbers, arise in the study of cyclotomic fields. The author obtains prime factorizations of for , and of for . These new results extend some of his earlier efforts.
|11B68||Bernoulli and Euler numbers and polynomials|