1969 Canadian MO Problems/Problem 8
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Problem
Let 
be a function with the following properties:
1) 
is defined for every positive integer 
;
2) is an integer;
3) 
;
4) 
for all 
and ;
5) 
whenever 
.
Prove that 
.
Solution
It's easily shown that 
and 
. Since 
Now, assume that 
is true for all 
where 
It follows that 
Hence, 
, and by induction 
.
| 1969 Canadian MO (Problems) | ||
| Preceded by Problem 7 | 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | Followed by Problem 9 |
