Which is the 5-adic number$\sqrt{-1}$? Let $a$ and $b$ be defined by the following;
$a = \cdots 431212$,
$b = \cdots 013233$.
$a$ and $b$ satisfy $x^2 + 1 = 0$ in base $5$.
Which is the 5-adic integer $\sqrt{-1}$?
If $a$ is the 5-adic integer $\sqrt{-1}$, $b$ is the 5-adic integer $ -
 \sqrt{-1}$?
If $b$ is the 5-adic integer $\sqrt{-1}$, $a$ is the 5-adic integer $ -
 \sqrt{-1}$?

Either $a$ or $b$ can be used as $\sqrt{-1}$.
