MathDB

IMO ShortList 2001, number theory problem 2

Source: IMO ShortList 2001, number theory problem 2

September 30, 2004

number theorycalculusIMO Shortlistalgebraquadratics

Problem Statement

Consider the system \begin{align*}x + y &= z + u,\\2xy & = zu.\end{align*} Find the greatest value of the real constant

m

such that

m \leq x/y

for any positive integer solution

(x,y,z,u)

of the system, with

x \geq y