An analog of Wolstenholme's Theorem: an addendum

Boaz Cohen

Vol. 29 No. 1 (2024)

Regular Articles

An analog of Wolstenholme's Theorem: an addendum

Published 2024-03-12

Boaz Cohen

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Abstract

Let p>=2 be a prime number and let a,b,m be positive integers such that p does not divide m. In a recent paper [1] we discussed the maximal prime power p^e, which divides the numerator of the fraction 1/m+1/(m+p^b)+1/(m+2p^b)+...+1/(m+(p^a-1)p^b), when written in reduced form. This short note may be regarded as an addendum to the paper~[1] for the case where p=2, b=1, m>1 and 2^a||m-1, which was left open.

Keywords

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

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