A note on the numerators of the Bernoulli numbers. (English) Zbl 0738.11024

Robert, A.

Expo. Math. 9, No. 2, 189-191 (1991).

This note mentions another proof of a theorem of von Staudt (1845): “If \(k\) is even \(\geq2\), \(p\) a prime with \((p-1)† k\) and \(p^ r\mid k\), then \(p^ r\mid N_ k\)”, where \(N_ k\) designates the numerator of the Bernoulli number \(B_ k\). Recently, K. Girstmair [Am. Math. Mon. 97, 136-138 (1990; see the preceding review)] has given a new proof, too. The author’s proof makes use of a p-adic version of the mean value theorem.

Reviewer: L.Skula (Brno)

MSC:

11B68

Bernoulli and Euler numbers and polynomials

Keywords:

von Staudt theorem; numerator; Bernoulli number; p-adic version of the mean value theorem

Citations:

Zbl 0738.11023