Let's find an integer such that the difference between its fifth power and three times its square is equal to 216.
According to the problem:

$$
x^{5}-3 x^{2}=216
$$

or

$$
x^{2}\left(x^{3}-3\right)=216
$$

Since 216 is divisible by 3, either $x^{2}$ or $x^{3}-3$ must also be divisible by 3; one condition would otherwise encompass the other. However, $x$ can only be 3, because for any multiple of 3 greater than 3, $x^{5}-3 x^{2}$ would be greater than 216.

The problem was solved by: Heymann Tivadar and Imre János.