Problem (Number Theory):
The product of the first five terms of a geometric progression is 32 . If the fourth term is 17 , compute the second term.

Solution:
Let $a$ be the third term of the geometric progression, and let $r$ be the common ratio. Then the product of the first five terms is

$$
\left(a r^{-2}\right)\left(a r^{-1}\right)(a)(a r)\left(a r^{2}\right)=a^{5}=32
$$

so $a=2$. Because the fourth term is $17, r=\frac{17}{a}=\frac{17}{2}$. The second term is $a r^{-1}=\frac{2}{17 / 2}=\frac{4}{17}$.

Final answer: $\frac{4}{17}$