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On three questions concerning $0, 1$ -polynomials

Michael Filaseta; Carrie Finch; Charles Nicol — 2006

Journal de Théorie des Nombres de Bordeaux

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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On three questions concerning 0 , 1 -polynomials

On three questions concerning $0, 1$ -polynomials