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Polynomials with Neccessary Equal Degrees

Source: Turkey TST 2016 P9

April 10, 2016
number theorypolynomial

Problem Statement

pp is a prime. Let KpK_p be the set of all polynomials with coefficients from the set {0,1,…,p−1}\{0,1,\dots ,p-1\} and degree less than pp. Assume that for all pairs of polynomials P,Q∈KpP,Q\in K_p such that P(Q(n))≡n(modp)P(Q(n))\equiv n\pmod p for all integers nn, the degrees of PP and QQ are equal. Determine all primes pp with this condition.
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