Knödel number explained

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} \equiv 1 \pmod{m} .^[1] 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

n = m - \varphi(m) where \varphi is Euler's totient function.

Examples

n	Kn
1
2
3
4

Literature

• Book: Makowski, A . Generalization of Morrow's D-Numbers . 1963 . 71.
• Book: Ribenboim, Paulo . Paulo Ribenboim

. The New Book of Prime Number Records . Paulo Ribenboim . 1989 . Springer-Verlag . New York . 978-0-387-94457-9 . 101.

Notes and References

1. Web site: Weisstein. Eric W.. Knödel Numbers. 2021-09-14. mathworld.wolfram.com. en.