1991 USAMO Problems/Problem 4
Let where and are positive integers. Prove that .
[You may wish to analyze the ratio for real and integer .]
Let us assume without loss of generality that . We then note that Similarly,
We note that equations and imply that . Then , so Multiplying this inequality by , we have It then follows that Rearranging this inequality, we find that , as desired.
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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