Difference between revisions of "Carmichael function"
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=== Examples === | === Examples === | ||
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Evaluate <math>2009^{2009}\pmod{1000}</math>. | Evaluate <math>2009^{2009}\pmod{1000}</math>. |
Revision as of 11:55, 1 August 2022
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
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
.
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