Important: The numtheory package has been deprecated.  Use the superseding command NumberTheory[ImaginaryUnit] instead.

The function imagunit will find a square root of $-1\mathbf{mod}n$, if possible, otherwise it returns FAIL.

The command with(numtheory,imagunit) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{numtheory}\right)\:$

$\mathrm{imagunit}\left(5\right)$

$2$

$\mathrm{imagunit}\left(7\right)$

$\mathrm{FAIL}$