On the irreducibility of 0,1-polynomials of the form f(x)xⁿ + g(x)

• Autorzy: Michael Filaseta , Manton Matthews, Jr.
• Języki publikacji: EN

Abstrakty

EN

If f(x) and g(x) are relatively prime polynomials in ℤ[x] satisfying certain conditions arising from a theorem of Capelli and if n is an integer > N for some sufficiently large N, then the non-reciprocal part of f(x)xⁿ + g(x) is either identically ±1 or is irreducible over the rationals. This result follows from work of Schinzel in 1965. We show here that under the conditions that f(x) and g(x) are relatively prime 0,1-polynomials (so each coefficient is either 0 or 1) and f(0) = g(0) = 1, one can take N = deg g + 2max{deg f, deg g}.

Kategorie tematyczne

• 12D05: Polynomials: factorization
• 12E05: Polynomials (irreducibility, etc.)
• 11R09: Polynomials (irreducibility, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2004
• Tom: 99
• Numer: 1
• Strony: 1-5

Daty

wydano

2004

Twórcy

autor

Michael Filaseta

• Mathematics Department, University of South Carolina, Columbia, SC 29208, U.S.A.

autor

Manton Matthews, Jr.

• Mathematics Department, University of South Carolina, Columbia, SC 29208, U.S.A.

Identyfikatory

DOI

10.4064/cm99-1-1