316. Solve the equation

$$
x^{3}-y^{3}=x y+61
$$

in natural numbers $x, y$.
316. Answer: $x=5, y=6$. If $x=d+y$, where $d \geqslant 1$, then $(3 d-1) y^{2}+\left(3 d^{2}-d\right) y+d^{3}=61$, from which $d \leqslant 3$.