A simple proof of a curious congruence by Zhao

DOI10.1090/S0002-9939-05-07939-6zbMath1131.11006OpenAlexW2151352236MaRDI QIDQ5313326

Chun-Gang Ji

Publication date: 29 August 2005

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-05-07939-6

zbMATH Keywords

prime numberKummer congruenceWolstenholme's theoremcongruences involving Bernoulli numbers

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Congruences; primitive roots; residue systems (11A07) Primes (11A41)

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A family of super congruences involving multiple harmonic sums, Congruences for finite triple harmonic sums, Congruences involving alternating harmonic sums modulo p ^α q ^β, Bernoulli numbers, Wolstenholme's theorem, and \(p^5\) variations of Lucas' theorem, On a congruence involving harmonic series and Bernoulli numbers, A curious congruence modulo prime powers, Super congruence on harmonic sums, A generalization of a curious congruence on harmonic sums, A new curious congruence involving multiple harmonic sums, A congruence involving harmonic sums modulo pαqβ

Cites Work

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• Two \(p^ 3\) variations of Lucas' theorem
• Congruences concerning Bernoulli numbers and Bernoulli polynomials
• On congruences involving Bernoulli numbers and the quotients of Fermat and Wilson