Knödel number

Knödel number

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 "K""n". "K"1 are the Carmichael numbers, "K"2 are 4, 6, 8, 10, 12, 14, 22, 24, 26, 30, 34, 38, 46, ... OEIS|id=A050990, K_3 are 9, 15, 21, 33, 39, 51, 57, 63, 69, 87, 93, ... OEIS2C|id=A033553.

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. [http://mathworld.wolfram.com/KnoedelNumbers.html]


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