2002 AIME I Problems/Problem 12
From AoPSWiki
Problem
Let 
for all complex numbers 
, and let 
for all positive integers 
. Given that 
and 
, where 
and 
are real numbers, find 
.
Solution
Iterating 
we get:
From this, it follows that 
, for all 
. Thus
Thus 
.
See also
| 2002 AIME I (Problems • Resources) | ||
| Preceded by Problem 11 | Followed by Problem 13 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
