Question 87
Determine all integers $x$ such that
$$
\left\lfloor \frac{x}{2} \right\rfloor \cdot \left\lfloor \frac{x}{3} \right\rfloor \cdot \left\lfloor \frac{x}{4} \right\rfloor = x^2
$$
holds. (Note that $\lfloor y \rfloor$ is the largest integer not greater than $y$.)
$$
\left\lfloor \frac{x}{2} \right\rfloor \cdot \left\lfloor \frac{x}{3} \right\rfloor \cdot \left\lfloor \frac{x}{4} \right\rfloor = x^2
$$
holds. (Note that $\lfloor y \rfloor$ is the largest integer not greater than $y$.)