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

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

Zbl 0738.11023