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

The function msqrt will compute the square root of x $\mathbf{mod}n$. It finds an integer y such that $y^2=x\mathbf{mod}n$ if possible, otherwise it returns FAIL.

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

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

$\mathrm{msqrt}\left(3\,11\right)$

$5$

$\mathrm{msqrt}\left(3\,7\right)$

$\mathrm{FAIL}$