Carmichael number

Definition

A composite number Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle n>1} is termed an absolute pseudoprime' or Carmichael number if it satisfies the following condition:

• The Liouville-lambda function of $n$ divides $n-1$.
• For any natural number $a$ relatively prime to $n$, $n$ divides Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle a^{n-1}-1} .
• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n} is a Fermat pseudoprime to any base relatively prime to it.