Geovene A.C.

Which numbers are more among natural numbers from 1 to 1000000 inclusive: those representable as the sum of a perfect square and a perfect cube, or those not representable in such a form

#
Let $n=k^{2}+m^{3}$, where $k, m, n \in \mathbf{N}$, and $n \leq 10^{6}$. Clearly, then $k \leq 1000$, and $m \leq 100$. Therefore, the representation of interest can be given by no more than $10^{5}$ pairs $(k, m)$.

(It is actually much fewer numbers that satisfy the condition, as some pairs yield numbers $n$ greater than $10^{6}$, and some different pairs yield the same number $n$.)

## Answer

Not representable in such a form.