Séminaire Lotharingien de Combinatoire, B31h (1993), 5 pp.
[Formerly: Publ. I.R.M.A. Strasbourg, 1994/021, p. 87-93.]

Pierre-André Picon

Conservation of the Integrality of Certain Quotients by Iterated Substitutions of Lucas Numbers

Abstract. If we replace k by a Lucas number, (uk-vk)/(u-v), in certain integral quotients such as the binomial coefficients, the quotient remains integral. We show that this substitution may be repeated indefinitely, while preserving the integrality, for a very large class of quotients.

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