8. Find natural \(k\) and \(n\), if it is known that

\[
k n^{2}-k n-n^{2}+n=94
\]
8. Solution. Factoring the left and right sides of the equation, we get:

\[
(n-1) n(k-1)=1 \cdot 2 \cdot 47
\]

This equality in the domain of natural numbers is possible, obviously, only when \(n=2\) and \(k=48\).