On three questions concerning 0,1-polynomials
Journal de Théorie des Nombres de Bordeaux, Volume 18 (2006) no. 2, pp. 357-370.

We answer three reducibility (or irreducibility) questions for 0,1-polynomials, those polynomials which have every coefficient either 0 or 1. The first concerns whether a naturally occurring sequence of reducible polynomials is finite. The second is whether every nonempty finite subset of an infinite set of positive integers can be the set of positive exponents of a reducible 0,1-polynomial. The third is the analogous question for exponents of irreducible 0,1-polynomials.

Nous répondons à trois questions concernant la réductibilité (ou irréductibilité) de 0,1-polynômes, polynômes qui n’ont pour seuls coefficients que 0 ou 1. La première question est de déterminer si une suite de polynômes qui se présente naturellement est finie. Deuxièmement, nous discutons si tout sous-ensemble fini d’un ensemble infini de nombres entiers positifs peut être l’ensemble des exposants d’un 0,1-polynôme réductible. La troisième question est similaire, mais pour l’ensemble des exposants d’un polynôme irréductible.

Received:
Published online:
DOI: 10.5802/jtnb.549
Michael Filaseta 1; Carrie Finch 1; Charles Nicol 1

1 Mathematics Department University of South Carolina Columbia, SC 29208, USA
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Michael Filaseta; Carrie Finch; Charles Nicol. On three questions concerning ${0,1}$-polynomials. Journal de Théorie des Nombres de Bordeaux, Volume 18 (2006) no. 2, pp. 357-370. doi : 10.5802/jtnb.549. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.549/

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