Difference between revisions of "Carmichael function"
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The second definition of the Carmichael function is the least common multiples of all the factors of <math>\phi(n)</math>. It is written as <math>\lambda'(n)</math>. However, in the case <math>8|n</math>, we take <math>2^{\alpha-2}</math> as a factor instead of <math>2^{\alpha-1}</math>. | The second definition of the Carmichael function is the least common multiples of all the factors of <math>\phi(n)</math>. It is written as <math>\lambda'(n)</math>. However, in the case <math>8|n</math>, we take <math>2^{\alpha-2}</math> as a factor instead of <math>2^{\alpha-1}</math>. | ||
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Revision as of 10:54, 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
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 .
This article is a stub. Help us out by expanding it.