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...82 and again by C. Babbage [2] in 1819), is in fact equivalent to Wolstenholme’s result. In the following 150 years, Wolstenholme’s congruence has been generalized in many directions (see Meštrović =-=[18]-=- for a survey). This paper considers generalizations in two directions. The first direction treats a larger set of binomial coefficients, replacing 2p−1 with kp−1. In 1900 Glaisher [8] showed that for...

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...congruence for the binomial coefficient ( 2p−1 p−1 ) modulo p7 involving multiple harmonic sums. The proof utilizes a number of congruences of the form (⋆). Variations on this congruence are given in =-=[2]-=-, Sec. 2. Generalizations of Mestrovic’s congruence, holding modulo arbitrarily large powers of p, were given by the author in [4]. 1In fact this congruence holds modulo p2n+3 CONGRUENCES FOR VALUES O...