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

The size of the largest cyclic group generated by $g^i\mathbf{mod}n$ is given by lambda(n).

Carmichael's theorem states that $a^{\mathrm{\lambda }\left(n\right)}=1\mathbf{mod}n$ if $\gcd \left(a\,n\right)=1$.

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

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

$\mathrm{\lambda }\left(13\right)$

$12$

$\mathrm{\lambda }\left(200\right)$

$20$

$\mathrm{\lambda }\left(-105\right)$

$12$