2014 USAMO Problems
Contents
[hide]Day 1
Problem 1
Let be real numbers such that and all zeros and of the polynomial are real. Find the smallest value the product can take.
Problem 2
Let be the set of integers. Find all functions such that for all with .
Problem 3
Prove that there exists an infinite set of points in the plane with the following property: For any three distinct integers and , points , , and are collinear if and only if .