Find all natural numbers $x$, possessing the following property: from each digit of the number $x$ one and the same digit $a \neq 0$ can be subtracted (all digits of it are not less than $a$) and as a result, $(x-a)^{2}$ is obtained.
Note that from the number $x$, no less than $a$ is subtracted. Therefore, $x-a \geq(x-a)^{2}$, from which $x-a=0$ or $x-a=1$. Thus, only the numbers from 1 to 9 have the property described in the problem.

## Answer

$1,2,3,4,5,6,7,8,9$.