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REPRESENTING AN ELEMENT IN ${\mathbf{F} }_{q} [t] $ AS THE SUM OF TWO IRREDUCIBLES
Published online by Cambridge University Press: 23 May 2013
Abstract
A monic polynomial in ${\mathbf{F} }_{q} [t] $ of degree $n$ over a finite field ${\mathbf{F} }_{q} $ of odd characteristic can be written as the sum of two irreducible monic elements in ${\mathbf{F} }_{q} [t] $ of degrees $n$ and $n- 1$ if $q$ is larger than a bound depending only on $n$. The main tool is a sufficient condition for simultaneous primality of two polynomials in one variable $x$ with coefficients in ${\mathbf{F} }_{q} [t] $.
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- Research Article
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- Copyright © University College London 2013
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