代表作主要参考文献 : 粗体字文献为与代表作关系最直接、最密切的文献
[Carmichael
1910]
R. D. Carmichael, Note on a new number theory function, Bull. Amer. Math. Soc. 16 (1910),
232–238.
[Ramanujan 1915] S. Ramanujan, Highly
composite numbers [Proc. London Math. Soc. (2) 14 (1915), 347-409], Collected papers of Srinivasa
Ramanujan, AMS Chelsea Publ., Providence, RI, 2000,
78–128.
[ErdÖs 1944]
P. ErdÖs,
On highly composite numbers, J. London Math. Soc. 19 (1944),
130–133.
[ErdÖs
1956] P. ErdÖs, On pseudoprimes and
Carmichael numbers, Publ. Math. Debrecen 4 (1956), 201–206.
[Miller 1976] G. Miller, Riemann’s hypothesis and tests for primality, J. Comput. and System Sc. 13 (1976),
300-317.
[Williams 1977] H. C.Williams, On numbers analogous to the Carmichael numbers, Canad. Math. Bull., 20:1 (1977), 133-143.
[Baillie and Wagstaff 1980] R. Baillie and Samuel S. Wagstaff, Jr., Lucas pseudoprimes, Math.
Comp. 35 (1980), 1391-1417.
[Monier 1980] Louis Monier, Evaluation and comparison of two efficient
probabilistic primality testing algorithms, Theoretical Computer Science 12 (1980), 97-108.
[PSW1980] C. Pomerance,
J. L. Selfridge and Samuel S. Wagstaff, Jr., The
pseudoprimes to 25·109, Math. Comp. , 35
(1980), 1003-1026.
[Rabin 1980] M. O. Rabin, Probabilistic
algorithms for testing primality, J. Number Theory 12 (1980), 128-138.
[Knuth 1981] D. E. Knuth, The
art of computer programming : Semi-numerical
algorithms, Volume 2, 2nd ed., Addison Wesley, Reading Massachusetts,
1981.
[Hua 1982] L. K. Hua, An introduction to number theory, Springer-Verlag, New
York, 1982.
[Ireland and Rosen 1982] K. Ireland and M. Rosen,
A classical introduction to modern number theory, GTM84,
Springer-Verlag, New York, 1982.
[Jaeschke
1993] G. Jaeschke, On
strong pseudoprimes to several bases, Math. Comp., 61 (1993), 915-926.
[Pinch 1993] R. G. E. Pinch, The
Carmichael numbers up to 1015,
Math. Comp. 61 (1993),
381–389.
[Alford,
Granville and Pomerance 1994] W. R.
Alford, A. Granville and C. Pomerance, There are infinitely many Carmichael numbers, Annals of Math. 140 (1994), 703–722.
[Arnault
1995a] F. Arnault, Rabin-Miller primality test: Composite numbers which pass it, Math. Comp., Vol.64 (1995), pp.355-361.
[Arnault
1995b] F. Arnault, Constructing Carmichael numbers
which are strong pseudoprimes to several bases,
J. Symbolic Computation, Vol.20
(1995), pp.151-161.
[Arnault 1997] F. Arnault, The Rabin-Monier Theorem
for Lucas Pseudoprimes, Math. Comp., 66
(1997), pp.869-881.
[Grantham 1998] J. Grantham, A
Probable Prime Test with High Confidence, J. Number Theory, 72 (1998), 32-47.
[Dusart 1999] Pierre Dusart, The kth prime is greater than k(ln k +ln ln k
-1) for k ≥2, Math.
Comp. 68 (1999), 441-445.
[Rosen 2000] Kenneth
H. Rosen, Elementary number theory and
its applications, 4th ed., Addison Wesley Longman, 2000.
[Chen and Greene] Zhuo
Chen and John Greene, Some comments on Baillie-PSW pseudoprimes, Fibonacci
Quart. 41 (2003), 334–344.
[Guy 2004] Richard. K. Guy, Unsolved
Problems in Number Theory, 3rd ed., Springer-Verlag,
New York, 2004.
[ Crandall and Pomerance 2005]
R. Crandall and C. Pomerance, Prime
numbers, a computational perspective, 2nd ed., Springer-Verlag,
New York, 2005.
[Grantham
2001] J. Grantham, Frobenius Pseudoprimes, Math.
Comp.,
70 (2001), 873-891.
[Pinch 2007] Richard G. E. Pinch, The
Carmichael numbers up to 1021, in
Proceedings of Conference on Algorithmic Number
Theory 2007 (edited by Anne-Maria Ernvall-Hyt¨onen, Matti Jutila, Juhani Karhum¨aki and Arto Lepist¨o), Turku Centre for
Computer Science General Publication 46 (2007),
129–131.
[Echi 2007] Othman Echi, Williams
numbers (English, with English
and French summaries), C. R. Math. Acad. Sci. Soc. R. Can. 29 (2007), no. 2, 41–47.
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