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numtheory

 lambda
 Carmichael's lambda function

 Calling Sequence lambda(n)

Parameters

 n - integer

Description

 • Important: The numtheory[lambda] command has been deprecated.  Use the superseding command NumberTheory[CarmichaelLambda] instead.
 • The size of the largest cyclic group generated by ${g}^{i}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}n$ is given by lambda(n).
 • Carmichael's theorem states that ${a}^{\mathrm{\lambda }\left(n\right)}=1\mathbf{mod}n$ if $\mathrm{gcd}\left(a,n\right)=1$.
 • The command with(numtheory,lambda) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{numtheory}\right):$
 > $\mathrm{λ}\left(13\right)$
 ${12}$ (1)
 > $\mathrm{λ}\left(200\right)$
 ${20}$ (2)
 > $\mathrm{λ}\left(-105\right)$
 ${12}$ (3)