Question 116
Let $(a_{n})$ be a sequence of real numbers. Suppose that $a_{0}=1$ and that for every $n \geqslant 1$, $a_{n}$ is the smallest strictly positive solution of
$$
\left(a_{n}-a_{n-1}\right)\left(a_{n}+a_{n-1}-2 \sqrt{n}\right)=2 .
$$
Find the smallest integer $n$ such that $a_{n} \geqslant 2022$.
$$
\left(a_{n}-a_{n-1}\right)\left(a_{n}+a_{n-1}-2 \sqrt{n}\right)=2 .
$$
Find the smallest integer $n$ such that $a_{n} \geqslant 2022$.