Difference between revisions of "Carmichael function"
(→Examples) |
(→Examples) |
||
Line 25: | Line 25: | ||
[http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1363764#1363764] | [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1363764#1363764] | ||
− | <math>\phi{1000}</math> | + | <math>{\alpha{\boxed{\lambda{\boxed{\phi{(1000)}}}}}}</math> |
== Second Definition == | == Second Definition == |
Revision as of 00:43, 10 August 2019
There are two different functions called the Carmichael function. Both are similar to Euler's totient function .
First Definition
The Carmichael function is defined at
to be the smallest positive integer
such that
for all positive integers
relatively prime to
. The order of
always divides
.
This function is also known as the reduced totient function or the least universal exponent function.
Suppose . We have
Examples
This article is a stub. Help us out by expanding it.
Evaluate .
[1]
Second Definition
The second definition of the Carmichael function is the least common multiples of all the factors of . It is written as
. However, in the case
, we take
as a factor instead of
.
Examples
This article is a stub. Help us out by expanding it.