On the divisibility properties of certain binomial sums

JOURNAL OF NUMBER THEORY

卷:147

Article

He, Bing

关键词: Binomial coefficients;    Divisibility;    WZ method;   

DOI  :  10.1016/j.jnt.2014.07.008

来源: Elsevier

【 摘 要 】

For any integer n > 1, we prove that 2n(2n n)vertical bar Sigma(n-1)(k=0) (6k + 1) (2k k)(3) 2(8(n-k-1)) and 2n(2n n)vertical bar Sigma(n-1)(k=0) (120k(2) + 34k + 3)(2k k)(4)(4k 2k)2(16(n-k-1)). The first divisibility result confirms a conjecture of Z.-W. Sun. (C) 2014 Elsevier Inc. All rights reserved.

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