Variant 10.6.1. 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 $(a, 13)$ is good.

(b) (3 points) Find the number of good pairs for which $p$ is a prime number less than 20.
Answer: (a) any of the numbers $14,26,182$. (b) 24.