1972 USAMO Problems/Problem 4
Problem
Let denote a non-negative rational number. Determine a fixed set of integers , such that for every choice of ,
Solution
Note that when approaches , must also approach for the given inequality to hold. Therefore
which happens if and only if
We cross multiply to get . It's not hard to show that, since , , , , , and are positive integers, then , , and .
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See Also
1972 USAMO (Problems • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 | ||
All USAMO Problems and Solutions |