A Goldbach 3-primes theorem for polynomials of low degree over finite fields of characteristic 2 (Q1107574)

A monic polynomial M in one variable x over the finite field \({\mathbb{F}}_ q\) is called even if \(q=2\) and if x or \(x+1\) divides M; otherwise M is called odd. In this paper the author proves that every odd monic polynomial M of degree 2, 3, 4, 5, and 6 over every finite field \({\mathbb{F}}_ q\) of characteristic 2 can be written as a sum of three irreducible monic polynomials except in case \(M(x)=x^ 2+a\), \(a\in {\mathbb{F}}_ q\).