\[\boxed{\text{201\ (201).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ \frac{m^{2} - 6m + 10}{m - 3} =\]
\[= \frac{m^{2} - 6m + 9 + 1}{m - 3} =\]
\[= \frac{(m - 3)^{2} + 1}{m - 3} =\]
\[= \frac{(m - 3)^{2}}{m - 3} + \frac{1}{m - 3} =\]
\[= m - 3 + \frac{1}{m - 3}\]
\[m \in Z;\ \ m - 3 + \frac{1}{m - 3}\ \in Z\]
\[\frac{1}{m - 3}\ \in Z\ \ m - 3 \in \left\{ - 1;1 \right\}\]
\[\frac{m^{2} - 6m + 10}{m - 3} \in \left\{ - 2;2 \right\}.\]
\[Ответ:\ - 2;2.\]
\[\textbf{б)}\ \frac{(m - 4)^{2}}{m - 2} = \frac{m^{2} - 8m + 16}{m - 2} =\]
\[= \frac{m^{2} - 4m + 4 - 4m + 12}{m - 2} =\]
\[= \frac{(m - 2)^{2} - 4m + 8 + 4}{m - 2} =\]
\[= \frac{(m - 2)^{2}}{m - 2} - \frac{4m - 8}{m - 2} + \frac{4}{m - 2} =\]
\[= m - 2 - \frac{4(m - 2)}{m - 2} + \frac{4}{m - 2} =\]
\[= m - 2 - 4 + \frac{4}{m - 2} =\]
\[= m - 6 + \frac{4}{m - 2}\]
\[m \in Z,\ \ \ m - 6 + \frac{4}{m - 2} \in Z\]
\[\frac{4}{m - 2} \in Z\]
\[m - 2 \in \left\{ - 4;\ - 2;\ - 1;1;2;4 \right\}\]
\[m = - 2\]
\[m = 0\]
\[m = 1\]
\[m = 3\]
\[m = 4\]
\[m = 6\]
\[\frac{(m - 4)^{2}}{m - 2} \in \left\{ - 9,\ - 8,\ 0,\ 1 \right\}\]
\[Ответ:\ - 9;\ - 8;0;1.\]