Bernoulli Numbers, Wolstenholme's Theorem, and p^5 Variations of Lucas' Theorem

Jianqiang Zhao

doi:10.1016/j.jnt.2006.05.005

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Bernoulli Numbers, Wolstenholme's Theorem, and p^5 Variations of Lucas' Theorem

Jianqiang Zhao

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Abstract

In this note we shall improve some congruences of D.F. Bailey [Two p^3 variations of Lucas' Theorem, JNT 35(1990), pp. 208-215] to higher prime power moduli, by studying the relation between irregular pairs of the form (p,p-3) and refined version of Wolstenholme's theorem.

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Jianqiang Zhao. 2006-02-10. Bernoulli Numbers, Wolstenholme's Theorem, and p^5 Variations of Lucas' Theorem. https://doi.org/10.1016/j.jnt.2006.05.005

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