Geodesic
Conservation of the Integrality of Certain Quotients by Iterated Substitutions of Lucas Numbers
Séminaire lotharingien de combinatoire, Tome 31 (1993)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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: 
@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},
     publisher = {mathdoc},
     volume = {31},
     year = {1993},
     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
PB  - mathdoc
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
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_1993_31_a7/
%F SLC_1993_31_a7
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/