9. For each non-negative real $x$, we define $\lfloor x\rfloor$ as the integer part of $x$, that is, the largest integer less than or equal to $x$, and $\{x\}=x-\lfloor x\rfloor$ as the fractional part of $x$.

Let $p$ be a positive real non-integer solution of the equation $\{z\lfloor z\rfloor\}=2021\{z\}$. What is the second smallest possible value of $\lfloor p\rfloor$?
(A) 2021
(B) 2022
(C) 3033
(D) 4042
(E) 4043
9. The answer is $\mathbf{( E )}$. Let $n=\lfloor p\rfloor$ and $\alpha=\{p\}$. Then the equation can be rewritten as $\{n(n+\alpha)\}=$ $2021 \alpha$, or equivalently,

$$
\{n \alpha\}=2021 \alpha
$$

Since on the left we have a fractional part, which is $2021+2021 m \geq 4042$, and thus $n \geq 4043$. Indeed, it is verified that $p=4043+\frac{1}{2022}$ is a solution.