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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

Andreas O. Bender*
Affiliation:
Pohang Mathematics Institute, POSTECH, San 31 Hyoja-dong, Pohang 790-784, Republic of Korea email [email protected]
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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] $.

Type
Research Article
Copyright
Copyright © University College London 2013 

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