Difference between revisions of "1990 USAMO Problems/Problem 2"
m (→See also)
|Line 32:||Line 32:|
Latest revision as of 18:14, 18 July 2016
We define . Then the recursive relation holds for , as well.
Since for all nonnegative integers , it suffices to consider nonnegative values of .
We claim that the following set of relations hold true for all natural numbers and nonnegative reals : To prove this claim, we induct on . The statement evidently holds for our base case, .
Now, suppose the claim holds for . Then The claim therefore holds by induction. It then follows that for all nonnegative integers , is the unique solution to the equation .
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
|1990 USAMO (Problems • Resources)|
|1 • 2 • 3 • 4 • 5|
|All USAMO Problems and Solutions|