2008 USAMO Problems/Problem 5
(Kiran Kedlaya) Three nonnegative real numbers , , are written on a blackboard. These numbers have the property that there exist integers , , , not all zero, satisfying . We are permitted to perform the following operation: find two numbers , on the blackboard with , then erase and write in its place. Prove that after a finite number of such operations, we can end up with at least one on the blackboard.
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
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