The p-adic valuation of k-central binomial coefficients

Details The p-adic valuation of k-central binomial coefficients The p-adic valuation of k-central binomial coefficients

2008-11-13

arxiv.org/abs/0811.2028v1

Mathematics

Number Theory

11 pages

Scientific paper

The coefficients c(n,k) defined by (1-k^2x)^(-1/k) = sum c(n,k) x^n reduce to
the central binomial coefficients for k=2. Motivated by a question of H.
Montgomery and H. Shapiro for the case k=3, we prove that c(n,k) are integers
and study their divisibility properties.

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