Divisibility of the Sums of the Power of Consecutive Integers

2023/04/15 by He, Tian-Xiao, Shiue, Peter J. -S.
#05A15 #11B83 #11B99 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.07605

Abstract

We study the divisibility of the sums of the odd power of consecutive integers, S(m,k)=1^mk+2^mk+⋯+k^mk and 1^k+2^k+⋯+n^k for odd integers m and k, by using the Girard-Waring identity. Faulhaber's approach for the divisibilities is discussed. Some expressions of power sums in terms of Stirling numbers of the second kind are represented.

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