On Some Finite Sums with Factorials

Details On Some Finite Sums with Factorials On Some Finite Sums with Factorials

2004-04-27

arxiv.org/abs/math/0404487v1

FACTA UNIVERSITATIS; Ser. Math. Inform. 14 (1999) 1-10

Mathematics

Number Theory

10 pages

Scientific paper

The summation formula $$ \sum^{n-1}_{i=0}\epsilon^i i! (i^k+u_k) = v_k+\epsilon^{n-1} n! A_{k-1}(n) $$ $(\epsilon=\pm 1; k=1,2,...; u_k, v_k\in \msbm\hbox{Z}; A_{k-1}$ 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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