56. Does there exist a polynomial of the third degree

$$
p(x)=a x^{3}+b x^{2}+c x+d
$$

where $a, b, c, d$ are integers, $a \neq 0$, such that $p(15)=3, p(21)=12$?
$\triangle$ Here

$$
p(21)-p(15)=12-3=9, \quad 21-15=6 \text{.}
$$

It turned out that the difference $p(21)-p(15)$ is not divisible by $21-15$, which contradicts the statement of problem 55.

Answer: does not exist.