Displaying similar documents to “On the decomposition of x d + a e x e + ⋯ + a 1 x + a 0 .”

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

Michael Filaseta, Manton Matthews, Jr. (2004)

Colloquium Mathematicae

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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) =...

Solving quadratic equations over polynomial rings of characteristic two.

Jorgen Cherly, Luis Gallardo, Leonid Vaserstein, Ethel Wheland (1998)

Publicacions Matemàtiques

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We are concerned with solving polynomial equations over rings. More precisely, given a commutative domain A with 1 and a polynomial equation antn + ...+ a0 = 0 with coefficients ai in A, our problem is to find its roots in A. We show that when A = B[x] is a polynomial ring, our problem can be reduced to solving a finite sequence of polynomial equations over B. As an application of this reduction,...