1972 IMO Problems/Problem 5
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 .
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 
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