1972 IMO Problems/Problem 5
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Let and be real-valued functions defined for all real values of and , and satisfying the equation for all . Prove that if is not identically zero, and if for all , then for all .
Solution
Let be the least upper bound for for all . So, for all . Then, for all ,
Therefore, , so .
Since is the least upper bound for , . Therefore, .
Borrowed from [1]
See Also
1972 IMO (Problems) • Resources | ||
Preceded by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 6 |
All IMO Problems and Solutions |