1969 Canadian MO Problems/Problem 8
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 • | Followed by Problem 9 |