  We treat the following "polynomial moment problem": for a complex polynomial
P(z) and distinct complex numbers a,b such that P(a)=P(b) to describe
polynomials q(z)=Q'(z) orthogonal to all degrees of P(z) on the segment [a,b].
We show that if P(z) is indecomposable then there exists a polynomial R(z) such
that Q(z)=R(P(z)). We also prove some related results.
