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]


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать реферат

Look at other dictionaries:

  • Carmichael number — In number theory, a Carmichael number is a composite positive integer n which satisfies the congruence b^{n 1} equiv 1 pmod{n} for all integers b which are relatively prime to n (see modular arithmetic). They are named for Robert Carmichael. The… …   Wikipedia

  • Número de Knödel — Dado un número natural n, un número de Knödel es un número compuesto m con la propiedad de que cada i < m coprimo con m satisface . El conjunto de todos los números naturales dado n se denomina el conjunto de los números de Knödel Kn. Nótese… …   Wikipedia Español

  • List of mathematics articles (K) — NOTOC K K approximation of k hitting set K ary tree K core K edge connected graph K equivalence K factor error K finite K function K homology K means algorithm K medoids K minimum spanning tree K Poincaré algebra K Poincaré group K set (geometry) …   Wikipedia

  • Vienna — Wien redirects here. For other uses, see Wien (disambiguation). This article is about the capital of Austria. For other uses, see Vienna (disambiguation). Vienna Wien …   Wikipedia

  • Austria — This article is about the country. For other uses, see Austria (disambiguation). Österreich and Oesterreich redirect here. For the surname rendered in either of these two ways, see Österreich (surname). For the Austrian national anthem, whose… …   Wikipedia

  • Munich — For other uses of Munich or München , see Munich (disambiguation). München Munich …   Wikipedia

  • Nineteen Eighty-Four — This article is about the Orwell novel. For other uses, see 1984 (disambiguation). Nineteen Eighty Four   …   Wikipedia

  • Sound symbolism — or phonosemantics is a branch of linguistics and refers to the idea that vocal sounds have meaning. In particular, sound symbolism is the idea that phonemes (the written representations of sounds, transcribed between slashes like this: /b/) carry …   Wikipedia

  • Jon Gerrard — Jon Gerrard, PC , MLA , BA, Ph.D , MD (born October 13, 1947) is a politician and medical doctor in Manitoba, Canada. He was a Member of Parliament (MP) from 1993 to 1997, and was a secretary of state in the government of Jean Chrétien. He has… …   Wikipedia

  • Italian cuisine — This article is part of the series …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”