An analog of Wolstenholme’s theorem

[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.

[学科分类] 工程和技术（综合）

[关键词] Wolstenholme's Theorem;Bauer's Theorem;Congruences;Primes