373. Find the condition under which the numbers $a, b, c$ represent the $k$-th, $n$-th, and $p$-th terms of the same geometric progression.
Given the problem,

$$
\frac{a}{b}=q^{k-n} ; \frac{a}{c}=q^{k-p}
$$

from which

$$
\begin{aligned}
& \left(\frac{a}{b}\right)^{k-p}=q^{(k-n)(k-p)} \\
& \left(\frac{a}{c}\right)^{k-n}=q^{(k-p)(k-n)}
\end{aligned}
$$

or

$$
\left(\frac{a}{b}\right)^{k-p}=\left(\frac{a}{c}\right)^{k-n}-\text { the desired condition. }
$$