MathDB
Polynomials (very bad name for a topic, I know...)

Source: Tournament of towns, Senior B-Level paper, Fall 2004

December 25, 2004
algebrapolynomialalgebra solved

Problem Statement

P(x) and Q(x) are polynomials of positive degree such that for all x P(P(x))=Q(Q(x)) and P(P(P(x)))=Q(Q(Q(x))). Does this necessarily mean that P(x)=Q(x)?