2012 Indonesia MO Problems/Problem 2
Problem
Let be an integer, and let be positive real numbers such that . Prove that
Solution
By AM-GM Substituting back into our original equation we get however, we only proved its , for the equality to happen, for all , which is impossible for all of them to be so, thus the equality is impossible
See Also
2012 Indonesia MO (Problems) | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 | Followed by Problem 3 |
All Indonesia MO Problems and Solutions |