How to prove this polynomial always has integer values at all integers

2015/09/29 by Wilberd van der Kallen, van der Kallen, Wilberd
Mathematics · #11B83 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B83

paper · pdf · doi:10.48550/arxiv.1509.08811

11 pages; reference corrected

arxiv created 2015/09/30 · arxiv updated 2015/10/01

Abstract

The following problem was posed by user "Kevin" on Mathoverflow. How to prove this polynomial always has integer values at all integers? P_m(x)=∑_i=0^m∑_j=0^m \binomx+jj \binomx-1j \binomji \binommi \binomim-j (3)/((2i-1)(2j+1)(2m-2i-1)). We provide an answer.

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