On the mod $p^7$ determination of ${2p-1\choose p-1}$

Details On the mod $p^7$ determination of ${2p-1\choose p-1}$ On the mod $p^7$ determination of ${2p-1\choose p-1}$

2011-08-04

arxiv.org/abs/1108.1174v1

Mathematics

Number Theory

Scientific paper

In this paper we prove that for any prime $p\ge 11$ holds $$ {2p-1\choose p-1}\equiv 1 -2p \sum_{k=1}^{p-1}\frac{1}{k} +4p^2\sum_{1\le i

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