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Cyclotomic polynomial as a composition!

Source: Romania TST 2014 Day 4 Problem 2

January 21, 2015
algebrapolynomialalgebra unsolved

Problem Statement

Let pp be an[color=#FF0000] odd prime number. Determine all pairs of polynomials ff and gg from Z[X]\mathbb{Z}[X] such that f(g(X))=∑k=0p−1Xk=Φp(X).f(g(X))=\sum_{k=0}^{p-1} X^k = \Phi_p(X).
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