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Representing an element in F_q[t] as the sum of two irreducibles

Research paper by Andreas O. Bender

Indexed on: 01 Mar '13Published on: 01 Mar '13Published in: Mathematics - Number Theory



Abstract

A monic polynomial in F_q[t] of degree n over a finite field F_q of odd characteristic can be written as the sum of two irreducible monic elements in 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 F_q[t].