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REPRESENTING AN ELEMENT IN ${\mathbf{F} }_{q} [t] $ AS THE SUM OF TWO IRREDUCIBLES

  • Andreas O. Bender (a1)

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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REPRESENTING AN ELEMENT IN ${\mathbf{F} }_{q} [t] $ AS THE SUM OF TWO IRREDUCIBLES

  • Andreas O. Bender (a1)

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