1989 USAMO Problems/Problem 1
For each positive integer , let Find, with proof, integers such that and .
We note that for all integers ,
It then follows that
If we let , we see that is a suitable solution.
Notice that it is also possible to use induction to prove the equations relating and with .
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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