8. Find the number of ordered pairs $(x, y)$ of positive integers satisfying $x y+x=y+92$.
Answer: 3
Solution: We manipulate the equation to form $x y+x-y-1=91$ or $(x-1)(y+1)=91$. Since $x$ and $y$ must be positive integers, and $91=7 \times 13$, we must have
$$
\left\{\begin{array} { l } 
{ x - 1 = 1 } \\
{ y + 1 = 9 1 }
\end{array} \quad \left\{\begin{array} { l } 
{ x - 1 = 9 1 } \\
{ y + 1 = 1 }
\end{array} \quad \left\{\begin{array} { l } 
{ x - 1 = 7 } \\
{ y + 1 = 1 3 }
\end{array} \quad \left\{\begin{array}{l}
x-1=13 \\
y+1=7
\end{array}\right.\right.\right.\right.
$$

Each of these systems of equations, except the second, yields a valid ordered pair $(x, y)$, so the answer is 3 .