Mean divisibility of multinomial coefficients

JOURNAL OF NUMBER THEORY

卷:136

Article

Akiyama, Shigeki

关键词: Multinomial coefficient;    Divisibility;    Riemann sum;   

DOI  :  10.1016/j.jnt.2013.10.005

来源: Elsevier

【 摘 要 】

Let m(1),..., m(s) be positive integers. Consider the sequence defined by multinomial coefficients: [GRAPHICS] Fix a positive integer k >= 2. We show that there exists a positive integer C(k) such that coproduct(t)(n=1) a(kn)/coproduct(t)(n=1) a(n) is an element of 1/C(k)Z for all positive integer t, if and only if GCD(m(1),..., m(s)) = 1. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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