On Some Finite Sums with Factorials

2004/04/27 by Branko Dragovich
Mathematics · Physics and Astronomy · #math.NT #math-ph #math.MP #msc:11A05

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published as FACTA UNIVERSITATIS; Ser. Math. Inform. 14 (1999) 1-10 · 10 pages

arxiv created 2004/04/27 · arxiv updated 2009/12/01

Abstract

The summation formula ∑^n-1_i=0εⁱ i! (i^k+u_k) = v_k+ε^n-1 n! A_k-1(n) (ε=± 1; k=1,2,...; u_k, v_k∈ \msbm\hboxZ; A_k-1 is a polynomial) is derived and its various aspects are considered. In particular, divisibility with respect to n is investigated. Infinitely many equivalents to Kurepa's hypothesis on the left factorial are found.

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