Carmichael function
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
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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
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