Carmichael number: Difference between revisions

Revision as of 17:15, 22 April 2009

A composite number $n>1$ is termed an Carmichael number or absolute pseudoprime if it satisfies the following condition:

The universal exponent (also called the Carmichael function) $\lambda (n)$ of $n$ divides $n-1$ .
For any natural number $a$ relatively prime to $n$ , $n$ divides $a^{n-1}-1$ .
$n$ is a Fermat pseudoprime to any base relatively prime to it.

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 A composite number <math>n > 1</math> is termed an '''Carmichael number''' or '''absolute pseudoprime''' if it satisfies the following condition:
-* The [[defining ingredient::Liouville-lambda function]] of <math>n</math> divides <math>n - 1</math>.
+* The [[defining ingredient::universal exponent]] (also called the Carmichael function) <math>\lambda(n)</math> of <math>n</math> divides <math>n - 1</math>.
 * For any natural number <math>a</math> relatively prime to <math>n</math>, <math>n</math> divides <math>a^{n-1} - 1</math>.
 * <math>n</math> is a [[defining ingredient::Fermat pseudoprime]] to any base relatively prime to it.