The p-Adic Valuation of Lucasnomials When p is a Special Prime
Laboratoire de Mathématiques Nicolas Oresme
To determine the p
-adic valuation of a Lucasnomial
i.e., of a generalized binomial coefficient with respect to a fundamental
Lucas sequence U
), there is an adequate Kummer rule if p
a regular prime. No such rule exists if p
is a special prime, i.e.,
We provide a complete description of the
-adic valuation of Lucasnomials when p
is special, with some
numerical examples. Applications to the integrality of generalized
Lucasnomial Fuss-Catalan numbers, Lucasnomial ballot and Lucasnomial
Lobb numbers are also given.
Full version: pdf,
Received July 3 2020; revised versions received December 12 2020; December 31 2020.
Published in Journal of Integer Sequences,
December 31 2020.
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