Divisibility of the Sums of the Power of Consecutive Integers

Tian-Xiao He, Peter J. -S. Shiue

We study the divisibility of the sums of the odd power of consecutive integers, $S(m,k)=1^{mk}+2^{mk}+\cdots +k^{mk}$ and $1^k+2^k+\cdots +n^k$ for odd integers $m$ and $k$, by using…