Quadratic polynomials and a set of integers
Source: Central American Olympiad 2007, Problem 3
June 12, 2007
quadraticsalgebrapolynomialalgebra proposed
Problem Statement
Let be a finite set of integers. Suppose that for every two different elements of , and , there exist not necessarily distinct integers , , belonging to , such that and are the roots of the polynomial . Determine the maximum number of elements that can have.