Knödel number

The Knödel numbers Kn for a given positive integer n are the set of composite integers m>n such that any b<m coprimeMathworldPlanetmath to m satisfies bm-n1modm. The Carmichael numbersMathworldPlanetmath are K1. There are infinitely many Knodel number Kn for a given n, something which was first proven only for n>2. Erdős speculated that this was also true for n=1 but two decades passed before this was conclusively proved by Alford, Granville and Pomerance.


  • 1 W. R. Alford, A. Granville, and C. Pomerance. “There are Infinitely Many Carmichael Numbers” Annals of Mathematics 139 (1994): 703 - 722
  • 2 P. Ribenboim, The Little Book of Bigger Primes, (2004), New York: Springer-Verlag, p. 102.
Title Knödel number
Canonical name KnodelNumber
Date of creation 2013-03-22 16:06:54
Last modified on 2013-03-22 16:06:54
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 6
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A51
Synonym Knodel number