LAUSR

Abstract We show that an element f in the ring Z [ [ x ] ] of formal power series over the integers is a sum of two irreducible elements in Z [ [ x ] ] if and only if the constant term of f is of the form ± p k ± q l or of the form ± p k , where p , q are prime numbers and k , l are positive integers. Moreover, if f 0 is of such form, then there exist 2 ℵ 0 pairwise coprime elements g ∈ Z [ [ x ] ] such that both g and g + f are irreducible.