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Solutions on the interval

Author: daniyar
Problem has been solved: 53 times

Русский язык | English Language



For some positive real number $ a $, let $ n $ be the number of different solutions $ (x_1, x_2, ..., x_ {2020}) $ of the equation $ \sum_ {i = 1} ^ {2020} \frac {(x_i ^ 2 + (a-x_i) ^ 2)} {a ^ 2} = 2020 $ if it is known that they all lie on the interval $ [0, a] $. Find the number of different positive integer divisors of $ n $.





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