Bobo is facing a strange optimization problem. Given n, m, he is going to find a real number αalphaα such that fff is maximized, where f=mini,j∈Z∣injm+t∣f = min_{i, j in mathbb{Z}} |frac{i}{n} - frac{j}{m} + t|f=mini,j∈Z∣nimj+t∣. Help him!
Bobo is facing a strange optimization problem. Given n, m, he is going to find a real number αalphaα such that f(12+α)f(frac{1}{2} + alpha)f(21+α) is maximized, where f(t)=mini,j∈Z∣in−jm+t∣f(t) = min_{i, j in mathbb{Z}} |frac{i}{n} - frac{j}{m} + t|f(t)=mini,j∈Z∣ni−mj+t∣. Help him! Note: It can be proved that the result is always rational.
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