Supercongruences involving Ap\'ery-like numbers and Bernoulli numbers

Ji-Cai Liu

Supercongruences involving Ap\'ery-like numbers and Bernoulli numbers

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arxiv 2403.19503 v2 pith:PLEA3FKO submitted 2024-03-28 math.NT

Ji-Cai Liu This is my paper · ORCID

classification math.NT

keywords numbersbernoulliery-likesupercongruenceskindsanotherconjecturalestablish

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We establish supercongruences for two kinds of Ap\'ery-like numbers, which involve Bernoulli numbers and Bernoulli polynomials. Conjectural supercongruences of the same type for another four kinds of Ap\'ery-like numbers are also proposed.

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Higher-Order Congruence for Reciprocal Power Sums and Generalized Lehmer-Type Products
math.NT 2026-07 accept novelty 4.5 of 10

Odd-order reciprocal power sums satisfy a uniform Bernoulli-polynomial congruence modulo n, and Lehmer-type products admit truncated Bell-polynomial expansions modulo n^{K+1}.

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