1981 IMO Problems/Problem 6
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Problem
The function 
satisfies
(1) 
(2) 
(3) 
for all non-negative integers 
. Determine 
.
Solution
We observe that 
and that 
, so by induction, 
. Similarly, 
and 
, yielding 
.
We continue with 
; 
; 
; and 
; 
.
It follows that 
when there are 1984 2s, Q.E.D.
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
| 1981 IMO (Problems) | ||
| Preceded by Problem 5 | 1 • 2 • 3 • 4 • 5 • 6 | Followed by Last question |
