STATUS
reviewed
approved
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Revision History for A002997
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Carmichael numbers: composite numbers k such that a^(k-1) == 1 (mod k) for every a coprime to k.
(history; published version)
(history; published version)
STATUS
proposed
reviewed
STATUS
editing
proposed
LINKS
W. R. Alford, Jon Grantham, Steven Hayman , and Andrew Shallue, <a href="https://doi.org/10.1090/S0025-5718-2013-02737-8">Constructing Carmichael numbers through improved subset-product algorithms</a>, Mathematics of Computation, Vol. 83, No. 286 (2014), pp. 899-915, <a href="http://arxiv.org/abs/1203.6664">arXiv preprint</a>, arXiv:1203.6664v1 [math.NT], Mar 29 2012.
W. R. Alford, A. Granville , and C. Pomerance, <a href="http://www.math.dartmouth.edu/~carlp/PDF/paper95.pdf">There are infinitely many Carmichael numbers</a>, Ann. of Math. (2) 139 (1994), no. 3, 703-722.
Sunghan Bae, Su Hu , and Min Sha, <a href="https://arxiv.org/abs/1809.05432">On the Carmichael rings, Carmichael ideals and Carmichael polynomials</a>, arXiv:1809.05432 [math.NT], 2018.
K. A. Draziotis, V. Martidis , and S. Tiganourias, <a href="https://arxiv.org/abs/2002.07095">Product Subset Problem: Applications to number theory and cryptography</a>, arXiv:2002.07095 [math.NT], 2020. See also <a href="https://doi.org/10.1142/9789811271922_0005">Chapter 5</a>, Analysis, Cryptography and Information Science, World Scientific (2023), p. 108.
A. Korselt, G. Tarry, I. Franel , and G. Vacca, <a href="http://oeis.org/wiki/File:Probl%C3%A8me_chinois.pdf">Problème chinois</a>, L'intermédiaire des mathématiciens 6 (1899), 142-144.
Carl Pomerance, J. L. Selfridge , and Samuel S. Wagstaff, Jr., <a href="http://dx.doi.org/10.1090/S0025-5718-1980-0572872-7">The pseudoprimes to 25*10^9</a>, Math. Comp., Vol. 35, No. 151 (1980), pp. 1003-1026.
Carl Pomerance & and N. J. A. Sloane, <a href="/A001567/a001567_4.pdf">Correspondence, 1991</a>.
LINKS
James Emery, <a href="http://www.stem2.org/je/numbertheory.pdf">Number Theory</a>, 2013. [Broken link]
LINKS
Fred Richman, <a href="https://web.archive.org/web/20230727074841/http
LINKS
James Emery, <a href="http://www.stem2.org/je/numbertheory.pdf">Number Theory</a>, 2013.
LINKS
François Arnault, <a href="https://web.archive.org/web/20000916022938/http
Renaud Lifchitz, <a href="http://www.primenumbers.net/Renaud/eng/korseltg.pdf">A generalization of the Korselt's criterion - Nested Carmichael numbers</a>.
<a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers.</a>.
REFERENCES
David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See entry 561 at p. 157.
STATUS
approved
editing
STATUS
editing
approved