74. The cathetus of a right-angled triangle is a perfect cube, the other cathetus represents the difference between this cube and its side (i.e., the first power), and the hypotenuse is the sum of the cube and its side. Find the sides.

## Problems of Iamblichus.
74. Diophantus' Solution. Let the hypotenuse be $x^{3}+x$, and the leg $x^{3}-x$.

Then the second leg will be:

$$
\sqrt{\left(x^{3}+x\right)^{2}-\left(x^{3}-x\right)^2}=2 x^{2}
$$

but $2 x^{2}=x^{3}$, therefore, $x=2$, the hypotenuse is 10, the first leg is 6, the second is 8.

Iamblichus (4th century) - one of the commentators on Nicomachus.