MathForces: Math Olympiads

# 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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