Knödel number

In number theory, an n-Knödel number for a given positive integer n is a composite number m with the property that each i < m coprime to m satisfies $$i^{m - n} \equiv 1 \pmod{m}$$. The concept is named after Walter Knödel.

The set of all n-Knödel numbers is denoted Kn. The special case K1 is the Carmichael numbers. There are infinitely many n-Knödel numbers for a given n.

Due to Euler's theorem every composite number m is an n-Knödel number for $$n = m-\varphi(m) $$ where $$ \varphi $$ is Euler's totient function.