Linear Forms in Monic Integer Polynomials

Abstract

Abstract. We prove a necessary and sufficient condition on the list of nonzero integers u1…, uk, k≥2, under which a monic polynomial f∊2ℤ[x] is expressible by a linear form u1 f1 + … + ukfk in monic polynomials f1…fk ∊ ℤ[x]. This condition is independent of f. We also show that if this condition holds, then the monic polynomials f1, … fk can be chosen to be irreducible in ℤ[x].