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Mathematics, 25.06.2019 03:50 darkremnant14

Thea has a key on her calculator marked $\textcolor{blue}{\bf\circledast}$. if an integer is displayed, pressing the $\textcolor{blue}{\bf\circledast}$ key chops off the first digit and moves it to the end. for example, if $6138$ is on the screen, then pressing the $\textcolor{blue}{\bf\circledast}$ key changes the display to $1386$. thea enters a positive integer into her calculator, then squares it, then presses the $\textcolor{blue}{\bf\circledast}$ key, then squares the result, then presses the $\textcolor{blue}{\bf\circledast}$ key again. after all these steps, the calculator displays $243$. what number did thea originally enter?

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