Title: When Does a Given Polynomial with Integer Coefficients Divide Another?
Abstract: Let f and g be polynomials with integer coefficients. In this paper, we improve upon a theorem of Nieto. We show that if the content of g divides the content of f and g(n) divides f (n) for an integer n arbitrarily chosen larger than some explicit constant depending on the coefficients and the degrees of f and g, then g divides f in ℤ[x]. In addition, given a polynomial f with integer coefficients, we provide a method to determine if f is irreducible over ℤ, and if not, find one of its divisors in ℤ [x].
Publication Year: 2016
Publication Date: 2016-01-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 2
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