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math.NT2010★ 5 cited
Factors of sums and alternating sums involving binomial coefficients and powers of integers
Victor J. W. Guo, Jiang Zeng
We study divisibility properties of certain sums and alternating sums involving binomial coefficients and powers of integers. For example, we prove that for all positive integers $…
math.NT2010★ 2 cited
New congruences for sums involving Apery numbers or central Delannoy numbers
Victor J. W. Guo, Jiang Zeng
The Apéry numbers and central Delannoy numbers are defined by $$A_n=\sum_{k=0}^{n}{n+k\choose 2k}^2{2k\choose k}^2, \quad D_n=\sum_{k=0}^{n}{n+k\choose 2k}{2k\choose k}…