Problem

Source: Romania TST 2014 Day 4 Problem 2

Tags: algebra, polynomial, algebra unsolved



Let $p$ be an odd prime number. Determine all pairs of polynomials $f$ and $g$ from $\mathbb{Z}[X]$ such that \[f(g(X))=\sum_{k=0}^{p-1} X^k = \Phi_p(X).\]