Knödel number

The Knödel numbers $K_{n}$ for a given positive integer $n$ are the set of composite integers $m>n$ such that any $b<m$ coprime to $m$ satisfies $b^{m-n}\\equiv 1\\mod m$ . The Carmichael numbers are $K_{1}$ . There are infinitely many Knodel number $K_{n}$ 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.

单词	KnodelNumber
释义	Knödel number The Knödel numbers $K_{n}$ for a given positive integer $n$ are the set of composite integers $m>n$ such that any $b<m$ coprime to $m$ satisfies $b^{m-n}\\equiv 1\\mod m$ . The Carmichael numbers are $K_{1}$ . There are infinitely many Knodel number $K_{n}$ 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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