2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64054We 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.8 pages, 2 figureComplex VariablesDynamical Systems30E99; 34C99text