A generalization of a curious congruence on harmonic sums

DOI10.1090/S0002-9939-06-08777-6zbMath1115.11006MaRDI QIDQ3425978

Tian Xin Cai, Xia Zhou

Publication date: 7 March 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

prime numberscongruences of harmonic sums

Mathematics Subject Classification ID

Congruences; primitive roots; residue systems (11A07) Primes (11A41)

Related Items (19)

PROOF OF A CONGRUENCE FOR HARMONIC NUMBERS CONJECTURED BY Z.-W. SUN ⋮ A family of super congruences involving multiple harmonic sums ⋮ On a congruence involving harmonic series and Bernoulli numbers ⋮ A curious congruence modulo prime powers ⋮ On the \(\pmod{p^7}\) determination of \({2p-1\choose p-1}\) ⋮ Super congruence on harmonic sums ⋮ Congruences for Apéry numbers βn =∑k=0nn k2n+k k ⋮ An extension of a congruence by Tauraso ⋮ Mod \(p\) structure of alternating and non-alternating multiple harmonic sums ⋮ $p$-adic $L$-functions and classical congruences ⋮ BERNOULLI NUMBERS AND CONGRUENCES FOR HARMONIC SUMS ⋮ Congruences arising from Apéry-type series for zeta values ⋮ Ohno-type identities for multiple harmonic sums ⋮ Congruences for central binomial sums and finite polylogarithms ⋮ Some families of supercongruences involving alternating multiple harmonic sums ⋮ Bowman-Bradley type theorem for finite multiple zeta values in \(\mathcal{A}_2\) ⋮ Congruences for Wolstenholme primes ⋮ A new curious congruence involving multiple harmonic sums ⋮ A congruence involving harmonic sums modulo pαqβ

Cites Work

• Unnamed Item
• Bernoulli numbers, Wolstenholme's theorem, and \(p^5\) variations of Lucas' theorem
• Congruences concerning Bernoulli numbers and Bernoulli polynomials
• On congruences involving Bernoulli numbers and the quotients of Fermat and Wilson
• A simple proof of a curious congruence by Zhao

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