Combinatorial congruences modulo prime powers

DOI10.1090/S0002-9947-07-04236-5zbMath1119.11016arXivmath/0508087MaRDI QIDQ3595030

Zhi-Wei Sun, Donald M. Davis

Publication date: 9 August 2007

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

Full work available at URL: https://arxiv.org/abs/math/0508087

zbMATH Keywords

congruencesbinomial coefficients

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Bernoulli and Euler numbers and polynomials (11B68) Congruences; primitive roots; residue systems (11A07) Polynomials (11S05)

Related Items

Supercongruences involving dual sequences, A note on the congruence $$\left( {_{mp^k }^{np^k } } \right) \equiv \left( {_m^n } \right)$$ (mod p r ), ON DIVISIBILITY OF BINOMIAL COEFFICIENTS, Binomial coefficients, roots of unity and powers of prime numbers, Divisibility by 2 of partial Stirling numbers, Factors of some lacunary \(q\)-binomial sums, Super congruences and Euler numbers, Fleck's congruence, associated magic squares and a zeta identity, Sharpness of exponent bounds for \(SU(n)\), LUCAS-TYPE CONGRUENCES FOR CYCLOTOMIC ψ-COEFFICIENTS, A generalization of the Gaussian formula and a \(q\)-analog of Fleck's congruence

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the sum \(\sum_{k\equiv r\pmod m}{n\choose k}\) and related congruences.
• A number-theoretic approach to homotopy exponents of \(\text{SU}(n)\)
• Two \(p^ 3\) variations of Lucas' theorem
• Combinatorial congruences and \(\psi\)-operators
• Some congruences for binomial coefficients
• General congruences for Bernoulli polynomials.
• Polynomial extension of Fleck's congruence