Difference between revisions of "2008 USAMO Problems/Problem 5"
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[[Category:Olympiad Number Theory Problems]] | [[Category:Olympiad Number Theory Problems]] |
Revision as of 18:58, 1 May 2008
Problem
(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.
Contents
[hide]Solution
Solution 1
Solution 2
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
Resources
2008 USAMO (Problems • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAMO Problems and Solutions |
- <url>viewtopic.php?t=202910 Discussion on AoPS/MathLinks</url>