Original scientific paper

An analog of Wolstenholme’s theorem

Boaz Cohen ; Department of Computer Science, The Academic College of Tel-Aviv, Israel

Abstract

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 \(1/m=1/(m+p^b)+...+1/(m+(p^a-1)p^b\), 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.

Keywords

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

Hrčak ID:

303379

URI

https://hrcak.srce.hr/303379

Publication date:

2.6.2023.

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