Question 22
For how many positive integers $n \le 1000$ is$$
\left\lfloor \dfrac{998}{n} \right\rfloor+\left\lfloor \dfrac{999}{n} \right\rfloor+\left\lfloor \dfrac{1000}{n}\right \rfloor
$$not divisible by $3?$ (Recall that $\lfloor x \rfloor$ is the greatest integer less than or equal to $x.$)
\left\lfloor \dfrac{998}{n} \right\rfloor+\left\lfloor \dfrac{999}{n} \right\rfloor+\left\lfloor \dfrac{1000}{n}\right \rfloor
$$not divisible by $3?$ (Recall that $\lfloor x \rfloor$ is the greatest integer less than or equal to $x.$)