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 represents the Carmichael numbers.

Every composite number m is a n-Knödel number for ${\displaystyle n=m-\varphi (m)}$.

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