Miklos Schweitzer 1951_10
Source:
October 8, 2008
algebrapolynomialmodular arithmeticRing Theory
Problem Statement
Let be a polynomial with integer coefficients and let 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}.