More congruences for central binomial coefficients
type: Item
instance of: scholarly article
title: More congruences for central binomial coefficients
zbMATH Open document ID: 1208.11027
author: Roberto Tauraso
published in: Journal of Number Theory
publication date: 2010-10-19T00:00:00Z
review text: Let \(p>5\) be a prime number. The author proves that \[ \sum_{k=1}^{p-1}\frac{1}{k^2}\binom{2k}{k}^{-1}\equiv\frac13 \frac{H(1)}{p}\pmod {p^3} \] and that \[ \sum_{k=1}^{p-1}\frac{(-1)^k}{k^3}\binom{2k}{k}^{-1}\equiv-\frac25 \frac{H(1)}{p^2}\pmod {p^3}, \] where \(H(1)=\sum_{k=1}^{p-1}\frac{1}{k}\).
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11B65
Mathematics Subject Classification ID: 11A07
zbMATH DE Number: 5802575
zbMATH Keywords: binomial coefficients
zbMATH Keywords: congruences
MaRDI profile type: Publication
full work available at URL: j.jnt.2010.06.004
OpenAlex ID: W2520018817
cites work: Borwein and Bradley's Apérv-Like Formulae for ζ(4n + 3)
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cites work: Congruences concerning Bernoulli numbers and Bernoulli polynomials
cites work: New congruences for central binomial coefficients
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cites work: Bernoulli numbers, Wolstenholme's theorem, and \(p^5\) variations of Lucas' theorem
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DOI: 10.1016/J.JNT.2010.06.004
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description: scientific article; zbMATH DE number 5802575