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Problem 2 of Second round - Polynomial and prime numbers

Source: VII International Festival of Young Mathematicians Sozopol 2016, Theme for 10-12 grade

August 31, 2019
algebrapolynomialprime numbersnumber theory

Problem Statement

We are given a polynomial f(x)=x6−11x4+36x2−36f(x)=x^6-11x^4+36x^2-36. Prove that for an arbitrary prime number pp, f(x)≡0(modp)f(x)\equiv 0\pmod{p} has a solution.
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