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

Michael Filaseta, and Manton Matthews, Jr.. "On the irreducibility of 0,1-polynomials of the form f(x)xⁿ + g(x)." Colloquium Mathematicae 99.1 (2004): 1-5. <http://eudml.org/doc/285261>.

@article{MichaelFilaseta2004,
abstract = {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\}.},
author = {Michael Filaseta, Manton Matthews, Jr.},
journal = {Colloquium Mathematicae},
keywords = {non-reciprocal part; irreducibility; -polynomial},
language = {eng},
number = {1},
pages = {1-5},
title = {On the irreducibility of 0,1-polynomials of the form f(x)xⁿ + g(x)},
url = {http://eudml.org/doc/285261},
volume = {99},
year = {2004},
}

TY - JOUR
AU - Michael Filaseta
AU - Manton Matthews, Jr.
TI - On the irreducibility of 0,1-polynomials of the form f(x)xⁿ + g(x)
JO - Colloquium Mathematicae
PY - 2004
VL - 99
IS - 1
SP - 1
EP - 5
AB - 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}.
LA - eng
KW - non-reciprocal part; irreducibility; -polynomial
UR - http://eudml.org/doc/285261
ER -