Proof of Sun's conjecture on the divisibility of certain binomial sums

Victor J. W. Guo

Proof of Sun's conjecture on the divisibility of certain binomial sums

Number Theory 2013-01-22 v1

Authors: Victor J. W. Guo

Abstract

In this paper, we prove the following result conjectured by Z.-W. Sun: $(2n-1){3n\choose n}| \sum_{k=0}^{n}{6k\choose 3k}{3k\choose k}{6(n-k)\choose 3(n-k)}{3(n-k)\choose n-k}.$ by showing that the left-hand side divides each summand on the right-hand side.

Keywords

binomial sums divisibility Sun's conjecture combinatorial identities

Cite

@article{arxiv.1301.4877,
  title  = {Proof of Sun's conjecture on the divisibility of certain binomial sums},
  author = {Victor J. W. Guo},
  journal= {arXiv preprint arXiv:1301.4877},
  year   = {2013}
}

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5 pages

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