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

The function mroot computes the rth root of x $\mathbf{mod}p$. It finds an integer y such that $y^r=x\mathbf{mod}p$ if possible. Otherwise, it returns FAIL.

The order, r, of the root must be prime.

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

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

$\mathrm{mroot}\left(5\,11\,13\right)$

$8$

$\mathrm{mroot}\left(2\,3\,6\right)$

$2$