Elementary proof of congruences involving trinomial coefficients for Babbage and Morley
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Publication:6597975
Publication date: 4 September 2024
Published in: Online Journal of Analytic Combinatorics (Search for Journal in Brave)
Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Congruences; primitive roots; residue systems (11A07)
Cites Work
- On the \(\pmod{p^7}\) determination of \({2p-1\choose p-1}\)
- Congruences involving generalized central trinomial coefficients
- Bernoulli numbers, Wolstenholme's theorem, and \(p^5\) variations of Lucas' theorem
- On the theory of Fermat quotients \(\frac{a^{p-1}-1}p=q(a)\).
- On the residues of the sums of products of the first \(p 1\) numbers, and their powers, to modulus \(p^2\) or \(p^3\).
- Congruences relating to the sums of products of the first \(n\) numbers and to other sums of products.
- Note on the congruence \(2^{in}\equiv(-)^n(2n)!/(n!)^2\), where \(2n+1\) is a prime.
- Congruences involving Bernoulli and Euler numbers
- Connection between ordinary multinomials, generalized Fibonacci numbers, partial Bell partition polynomials and convolution powers of discrete uniform distribution
- Generalization of Wolstenholme's and Morley's congruences
- On the converse of Wolstenholme's Theorem
- Some congruences for trinomial coefficients
- Some congruences involving binomial coefficients
- On binomial coefficients modulo squares of primes
- Note on a Theorem of Glaisher
- A Theorem of Glaisher
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