$29 \cdot 4$ A store prices an item in dollars and cents, and when a $4\%$ sales tax is added, the result is exactly $n$ dollars, so no rounding is necessary (i.e., $n$ is a positive integer). The smallest value of $n$ is
(A) 1 .
(B) 13 .
(C) 25 .
(D) 26 .
(E) 100 .
(31st American High School Mathematics Examination, 1980)
[Solution] Let $m$ be the price of the project calculated in points, then $1.04 m=100 n$.
Thus, $8 \cdot 13 m=100^{2} n$, so $m=2 \cdot 5^{4} \cdot \frac{n}{13}$.
Therefore, the necessary and sufficient condition for $m$ to be an integer is $13 \mid n$. Hence, the answer is $(B)$.