University of South Carolina High School Math Contest/1993 Exam/Problem 5
From AoPSWiki
Problem
Suppose that 
is a function with the property that for all 
and 
, 
and 
What is the value of 
?
Solution
Notice that 
. Also, 
. Thus, 
.
In general, 
, so we have a simple recursive definition for the function . From here we can see that 
for all positive integers 
.
