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 ≡ 1 ( mod m ) {\displaystyle 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 − φ ( m ) {\displaystyle n=m-\varphi (m)} where φ {\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.