Séminaire lotharingien de combinatoire, Tome 31 (1993)
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Pierre-André Picon. Conservation of the Integrality of Certain Quotients by Iterated Substitutions of Lucas Numbers. Séminaire lotharingien de combinatoire, Tome 31 (1993). http://geodesic.mathdoc.fr/item/SLC_1993_31_a7/
@article{SLC_1993_31_a7,
author = {Pierre-Andr\'e Picon},
title = {Conservation of the {Integrality} of {Certain} {Quotients} by {Iterated} {Substitutions} of {Lucas} {Numbers}},
journal = {S\'eminaire lotharingien de combinatoire},
year = {1993},
volume = {31},
url = {http://geodesic.mathdoc.fr/item/SLC_1993_31_a7/}
}
TY - JOUR
AU - Pierre-André Picon
TI - Conservation of the Integrality of Certain Quotients by Iterated Substitutions of Lucas Numbers
JO - Séminaire lotharingien de combinatoire
PY - 1993
VL - 31
UR - http://geodesic.mathdoc.fr/item/SLC_1993_31_a7/
ID - SLC_1993_31_a7
ER -
%0 Journal Article
%A Pierre-André Picon
%T Conservation of the Integrality of Certain Quotients by Iterated Substitutions of Lucas Numbers
%J Séminaire lotharingien de combinatoire
%D 1993
%V 31
%U http://geodesic.mathdoc.fr/item/SLC_1993_31_a7/
%F SLC_1993_31_a7
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. The following versions are available:
