The other day I thought of this question:
Is it possible to find a set of palindromic numbers such that the square of them is itself palindromic? In other words:
$A = \{a : a^{2}=b$ where a,b are palindromic integers}
I'm not a mathematician so I don't really know where to begin!
Edit: Thanks to all who responded so quickly! My question now is whether is possible to find ALL possible integers that belongs to such set. Would it be possible to find a rule for that set?
If you keep to the digits $0, 1,$ and $2$, and include plenty of $0$'s you can make lot of examples.
$$1002001^2 = 1004006004001$$
$$212^2 = 44944$$