203. Nine digits. Find a nine-digit number, all digits of which are different and do not contain zero, and the square root of which has the form $\overline{a b a b c}$, where $\overline{a b}=c^{3}$.
203. The digit $c$ can only coincide with 3 or 4. However, the number $(64644)^{2}$ is ten-digit. Therefore, the only solution to our problem will be $(27273)^{2}=743816529$.

[N. Farnum, S. S. M., 63, 603 (October 1963).]

This solution will be unique even if we drop the restriction $a b=c^{3}$. Moreover, $27273=3(9091)$, and 9091 is the largest prime divisor of any square composed of nine distinct non-zero digits.