[ [Decimal number system ] $[$ Equations in integers $]$

Find a two-digit number that is equal to the sum of the cube of the number of its tens and the square of the number of its units.

#
Let's denote the number of tens by $x$, and the number of units by $y$. Then $10 x + y = x^3 + y^2$ or $x(10 - x^2) = y(y - 1)$, where $y(y - 1)$ is an even natural number. Therefore, $x$ is even and $10 - x^2 > 0$. Consequently, $x = 2$. Substituting into the equation, we find $y = 4$.

## Answer

24.

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