29 Find the least positive integer $n$ for which $\frac{n-10}{9 n+11}$ is a non-zero reducible fraction.
29 Answer: (111)
Consider $\frac{9 n+11}{n-10}=9+\frac{101}{n-10}$. If $\frac{n-10}{9 n+11}$ is a non-zero reducible fraction, then $\frac{101}{n-10}$ is also a non-zero reducible fraction $\Rightarrow$ Least positive integer $n=111$.