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

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

2003-03-26

arxiv.org/abs/math/0303332v3

J. of Number Theory 123 (2007), pp. 18-26.

Mathematics

Number Theory

7 pages. Final version accepted by J. of Number Theory

Scientific paper

10.1016/j.jnt.2006.05.005

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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