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

Wilberd van der Kallen

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arXiv · 1509.08811

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

Wilberd van der Kallen

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Abstract

The following problem was posed by user "Kevin" on Mathoverflow. How to prove this polynomial always has integer values at all integers? $$P_m(x)=\sum_{i=0}^{m}\sum_{j=0}^{m} \binom{x+j}{j} \binom{x-1}{j} \binom{j}{i} \binom{m}{i} \binom{i}{m-j} \frac{3}{(2i-1)(2j+1)(2m-2i-1)}.$$ We provide an answer.

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BibTeX RIS

Wilberd van der Kallen. 2015-09-29. How to prove this polynomial always has integer values at all integers. https://arxiv.org/abs/1509.08811

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