MathDB

Three nonnegative real numbers

r_1

r_2

r_3

are written on a blackboard. These numbers have the property that there exist integers

a_1

a_2

a_3

, not all zero, satisfying a_1r_1 \plus{} a_2r_2 \plus{} a_3r_3 \equal{} 0. We are permitted to perform the following operation: find two numbers

x

y

on the blackboard with

x \le y

, then erase

y

and write y \minus{} x in its place. Prove that after a finite number of such operations, we can end up with at least one

0

on the blackboard.

Problem Statement