59. Find the non-negative integer values of $n$ for which $\frac{30 n+2}{12 n+1}$ is an integer.
59. $\frac{30 n+2}{12 n+1}=\frac{(24 n+2)+6 n}{12 n+1}=2+\frac{6 n}{12 n+1}; \quad \frac{6 n}{12 n+1}$
will be an integer only when $n=0$, for other values of $n$ it is a proper fraction. Therefore, only when $n=0$ is $\frac{30 n+2}{12 n+1}$ an integer (2).