\[\boxed{\text{205\ (205).\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\frac{1}{a} + \frac{1}{b} = \frac{1}{7}\]
\[\frac{1}{a} = \frac{1^{\backslash b}}{7} - \frac{1^{\backslash 7}}{b}\]
\[\frac{1}{a} = \frac{b - 7}{7b}\]
\[a = 1\ :\frac{b - 7}{7b} = \frac{7b}{b - 7} =\]
\[= \frac{7b - 49 + 49}{b - 7} =\]
\[= \frac{7(b - 7) + 49}{b - 7} =\]
\[= \frac{7(b - 7)}{b - 7} + \frac{49}{b - 7} = 7 + \frac{49}{b - 7}.\]
\[a \in N\ \ при\ 7 + \frac{49}{b - 7} \in \text{N.}\]
\[\ \frac{49}{b - 7} \in N,\ то\ есть:\ \]
\[b - 7 = 1;7;49.\]
\[b = 14 \rightarrow \ a = 14;\]
\[b = 56 \rightarrow \ \ a = 8;\]
\[b = 8\ \rightarrow a = 56.\]
\[Ответ:(14;14),\ (8;56),\ (56;8).\]