590. The last two digits of the decimal representation of the square of some natural number are equal and different from zero. What are these digits? Find all solutions.
$\triangle$ The square of a natural number can end in the digits $0,1,4,5,6$ or 9. The digit 0 is not suitable in this case. Then the square can end in

$$
11,44,55,66,99
$$

However, cases where the square ends in 11, 55, or 99 are impossible, as if the last digit of the square of a natural number is odd, then the second-to-last digit must be even (see supporting problem 566). The case where the square ends in 66 is also ruled out, as based on the divisibility rules for 2 and 4, a natural number that ends in 66 is divisible by 2 but not by 4.

The remaining option is 44. The fact that the square of a natural number can end in 44 is demonstrated by the example $12^{2}=144$.

Answer: 4 and 4.