An analog of Wolstenholme's Theorem

Boaz Cohen


In this paper we shall prove an analogous version of Wolstenholme's theorem, namely, given a prime number p>=2 and positive integers a,b,m such that p|-m, we shall determine the maximal prime power p^e which divides the numerator of the fraction


when written in reduced form, with the exception of one case, where p=2, b=1, m>1 and 2^a||m-1. In this exceptional case, a lower bound for e is given.


Wolstenholme's Theorem, Bauer's Theorem, Congruences, Primes

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ISSN: 1331-0623 (Print), 1848-8013 (Online)