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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.

Examples※

References※

Literature※

• Makowski, A (1963). Generalization of Morrow's D-Numbers. p. 71.
• Ribenboim, Paulo (1989). The New Book of Prime Number Records. New York: Springer-Verlag. p. 101. ISBN 978-0-387-94457-9.

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