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Square-free Values of Decomposable Forms
Published online by Cambridge University Press: 20 November 2018
Abstract
In this paper we prove that decomposable forms, or homogeneous polynomials $F\left( {{x}_{1}}\,,\,.\,.\,.\,,\,{{x}_{n}} \right)$ with integer coefficients that split completely into linear factors over
$\mathbb{C}$, take on infinitely many square-free values subject to simple necessary conditions, and they have
$\text{deg}\,f\,\le \,2n\,+\mid 2$ for all irreducible factors
$f$ of
$F$. This work generalizes a theorem of Greaves.
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- Research Article
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- Copyright © Canadian Mathematical Society 2018
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