MathNet 2020 — Math Olympiad Vault — Part 01 Question 112

Suppose that $a \gt 0$ and the minima of function $f(x) = x + \frac{100}{x}$ on intervals $(0, a]$ and $[a, +\infty)$ are $m_1, m_2$, respectively. If $m_1 m_2 = 2020$, then the value of $a$ is ______.