An analog of Wolstenholme’s theorem

Mathematical Communications

article

Boaz Cohen¹ 

[1] Department of Computer Science, The Academic College of Tel-Aviv

关键词: Wolstenholme's Theorem;    Bauer's Theorem;    Congruences;    Primes;   

学科分类：工程和技术（综合）

来源: Sveuciliste Josipa Jurja Strossmayera u Osijeku * Odjel za Matematiku / University of Osijek, Department of Mathematics

【 摘 要 】

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 shalldetermine the maximal prime power pe, which divides the numerator of the fraction 1m+1m + pb +1m + 2pb + . . . +1m + (pa − 1)pb,when written in reduced form, with the exception of one case, where p = 2, b = 1, m > 1and 2a∥m − 1. In this exceptional case, a lower bound for e is given.

【 授权许可】

CC BY-NC-ND