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 ${\displaystyle i^{m-n}\equiv 1{\pmod {m}}}$. The concept is named after Walter Knödel.

The set of all n-Knödel numbers is denoted K_n. 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 ${\displaystyle n=m-\varphi (m)}$ where ${\displaystyle \varphi }$ is Euler's totient function.