Three Integers
Source: Indonesia Mathematics Olympiad 2005 Day 2 Problem 6
June 2, 2008
symmetrygeometryinequalitiesnumber theory proposednumber theory
Problem Statement
Find all triples of integers which satisfy
x(y \plus{} z) \equal{} y^2 \plus{} z^2 \minus{} 2
y(z \plus{} x) \equal{} z^2 \plus{} x^2 \minus{} 2
z(x \plus{} y) \equal{} x^2 \plus{} y^2 \minus{} 2.