Variant 10.6.3. A pair of natural numbers ( $a, p$ ) is called good if the number $a^{3}+p^{3}$ is divisible by $a^{2}-p^{2}$, and $a>p$.

(a) (1 point) Indicate any possible value of $a$ for which the pair $(a, 19)$ is good.

(b) (3 points) Find the number of good pairs for which $p$ is a prime number less than 24.
Answer: (a) any of the numbers $20,38,380$. (b) 27.