NumberTheory
CarmichaelLambda
Carmichael's lambda function
Calling Sequence
Parameters
Description
Examples
Compatibility
CarmichaelLambda(n)
lambda(n)
λn
n
-
positive integer
The size of the largest cyclic group generated by gimodn is given by CarmichaelLambda(n).
Alternatively, CarmichaelLambda(n) is the smallest integer i such that for all g coprime to n, gi is congruent to 1 modulo n.
lambda is an alias for CarmichaelLambda.
You can enter the command lambda using either the 1-D or 2-D calling sequence. For example, lambda(8) is equivalent to λ8.
withNumberTheory:
seqTotienti,i=1..7
1,1,2,2,4,2,6
seqCarmichaelLambdai,i=1..7
CarmichaelLambda8
2
Totient8
4
λ21
6
Totient21
12
CarmichaelLambdak
Carmichael's theorem states that gλn is congruent to 1 modulo n if g and n are coprime.
d≔CarmichaelLambda112
d≔12
seq`if`igcdg,112=1,gdmod112,NULL,g=1..111
1
The NumberTheory[CarmichaelLambda] command was introduced in Maple 2016.
For more information on Maple 2016 changes, see Updates in Maple 2016.
See Also
NumberTheory[Totient]
Download Help Document