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Michael Filaseta; Carrie Finch; Charles Nicol
On three questions concerning ${0,1}$-polynomials
Journal de théorie des nombres de Bordeaux, 18 no. 2 (2006), p. 357-370, doi: 10.5802/jtnb.549
Article PDF | Reviews MR 2289429 | Zbl 05135395

Résumé - Abstract

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.

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