Divisibility of some binomial sums

2018/08/09 by He-Xia Ni, Hao Pan, Ni, He-Xia +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1808.03213

openalex publication_date 2018/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

With help of q-congruence, we prove the divisibility of some binomial sums. For example, for any integers ρ,n≥ 2, ∑_k=0^n-1(4k+1) \binom2kk^ρ⋅ (-4)^ρ(n-1-k) ≡ 0\pmod2^ρ-2n\binom2nn.

Citations

• Kind of proofs of Ramanujan-like series

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