Question 79
Determine all positive integers $n$ such that
$$
\lfloor \sqrt[4]{1} \rfloor + \lfloor \sqrt[4]{2} \rfloor + \dots + \lfloor \sqrt[4]{n} \rfloor = \frac{3}{2}n + 1.
$$
$$
\lfloor \sqrt[4]{1} \rfloor + \lfloor \sqrt[4]{2} \rfloor + \dots + \lfloor \sqrt[4]{n} \rfloor = \frac{3}{2}n + 1.
$$