Knödel number

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A 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} \equiv 1 \mod m. The set of all such integers for n is then called the set of Knödel numbers Kn. K1 are the Carmichael numbers, K2 are 4, 6, 8, 10, 12, 14, 22, 24, 26, 30, 34, 38, 46, ... (sequence A050990 in OEIS), K3 are 9, 15, 21, 33, 39, 51, 57, 63, 69, 87, 93, ... A033553.

[edit] References

  • Makowski, A. "Generalization of Morrow's D-Numbers." Simon Stevin 36, (1963): 71
  • Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag (1989): 101
  • Weisstein, Eric W. "Knödel Numbers." From MathWorld--A Wolfram Web Resource. [1]
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