2. (2006 Thailand Mathematical Olympiad) Find all integers $n$, such that $n^{2}+59 n+881$ is a perfect square.
2. Let $n^{2}+59 n+881=m^{2}$ (where $m$ is an integer), then $4 m^{2}=(2 n+59)^{2}+43$, which means $(2 m+2 n+59)(2 m-2 n-59)=43$.

Since 43 is a prime number, we have,
$$
\left\{\begin{array}{l}
2 m+2 n+59=43,-43,1,-1, \\
2 m-2 n-59=1,-1,43,-43 .
\end{array}\right.
$$

Solving this, we get $n=-40$ or -19.