Problem

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

Tags: algebra, polynomial, prime numbers, number theory



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