2009 Indonesia MO Problems/Problem 2
Problem
For any real , let be the largest integer that is not more than . Given a sequence of positive integers such that and Prove that holds for every positive integer .
Solution
By assuming we can conclude that:
Since , it is also true that , implying .
After repeating this same process to all given fractions, we get: which is a impossible statement because are all positive integers.
Therefore,
~NounZero
See Also
2009 Indonesia MO (Problems) | ||
Preceded by First Problem |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 | Followed by Problem 3 |
All Indonesia MO Problems and Solutions |