Let f(x) be a polynomial with integer coefficients and let p be a prime. Denote by z_1,...,z_{p\minus{}1} the (p\minus{}1)th complex roots of unity. Prove that
f(z_1)\cdots f(z_{p\minus{}1})\equiv f(1)\cdots f(p\minus{}1) \pmod{p}. algebrapolynomialmodular arithmeticRing Theory