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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,
(*u*^{k}-v^{k})/(*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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