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

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Filaseta M., Matthews M.

Colloquium Mathematicum

2004

tom 99

nr 1

1-5

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}.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Filaseta M.

1 Matthews M.

1 2004

Wyniki wyszukiwania

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