6. How many integers $m$ in the range from 1 to 1996 are there such that $\frac{m^{2}+7}{m+4}$ is not a reduced fraction?
6. According to the problem, we should have $d=\left(m^{2}+7, m+4\right)>1$, so $\left(m^{2}+7, m+4\right)=23$. Since 23 | $(m+4)$, and $5 \leqslant m+4 \leqslant 2000$, we know that in the range from 1 to 1996, there are $\left[\frac{2000}{23}\right]-\left[\frac{5}{23}\right]$ $=86$ such $m$ values.