573. Do there exist natural numbers $a, b$, and $c$ such that the decimal representation of the sum

$$
a^{60}+b^{60}+c^{60}
$$

ends in the digit 9?

574. Prove that the square of a two-digit number $\overline{a b}(b \neq 0)$ ends in $\overline{a b}$ only when $\overline{a b}$ is 25 or 76.