Abstract
Soit ϕ(x 1 ,...,x h ,y) = u 1 x 1 + ... + u h x h + vy une forme lineaire a coefficients entiers non nuls u 1 ,..., u h , v. Soient A = (A 1 ,..., Ah) un h-uplet d'ensembles finis d'entiers et B un ensemble infini d'entiers. Definissons la fonction de representation associee a la forme ϕ et aux ensembles A et B comme suit: Si cette fonction de representation est constante, alors l'ensemble B est periodique, et la periode de B est bornee en termes du diametre de l'ensemble fini {ϕ(a 1 ,..., a h , 0): (a 1 ,..., a h ) ∈ A 1 x ... × A h }. D'autres resultats sur les ensembles se completant pour une forme lineaire sont egalement prouves.
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