2ag * Find all natural numbers $x$, such that $x^{2}$ is a twelve-digit number of the form: $2525 * * * * * * 89$ (the six “*”s represent six unknown digits, which are not necessarily the same).
The last two digits of the number $x$ can only be $17, 33, 67, 83$. Also, $2525 \cdot 10^{8} < x^{2} < 2526 \cdot 10^{8}$, which means $502493 < x < 502594$. Within this interval, the numbers whose last two digits are $17, 33, 67, 83$ are four: $502517, 502533, 502567, 502583$. Upon inspection, they meet the requirements.