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单词 KnodelNumber
释义

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.

References

  • 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.
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更新时间:2025/5/5 1:57:59