Polynomial of degree n in A[X] without roots in A
Source: Romanian District Olympiad 2006, Grade 12, Problem 3
March 11, 2006
algebrapolynomialsuperior algebrasuperior algebra solved
Problem Statement
Prove that if is a commutative finite ring with at least two elements and is a positive integer, then there exists a polynomial of degree with coefficients in which does not have any roots in .