OMCC 2020 Problem 1

A four-digit positive integer is called virtual if it has the form $\overline{abab}$ , where $a$ and $b$ are digits and $a \neq 0$ . For example 2020, 2121 and 2222 are virtual numbers, while 2002 and 0202 are not. Find all virtual numbers of the form $n^2+1$ , for some positive integer $n$ .