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Some pseudoprimes and related numbers having special forms


Author: Wayne L. McDaniel
Journal: Math. Comp. 53 (1989), 407-409
MSC: Primary 11A07; Secondary 11Y99
DOI: https://doi.org/10.1090/S0025-5718-1989-0968152-6
MathSciNet review: 968152
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Abstract: We give an example of a pseudoprime which is itself of the form $ {2^n} - 2$, answering a question posed by A. Rotkiewicz, show that Lehmer's example of an even pseudoprime having three prime factors is not unique, and answer a question of Benkoski concerning the solutions of $ {2^{n - 2}} \equiv 1\;\pmod n$.


References [Enhancements On Off] (What's this?)

  • [1] S. J. Benkoski, Review of "On the congruence $ {2^{n - k}} \equiv 1\;\pmod n$." MR 87e:11005.
  • [2] J. Brillhart, D. H. Lehmer, J. L. Selfridge, B. Tuckerman & S. S. Wagstaff, Jr., Factorizations of $ {b^n} \pm 1, b = 2,3,5,6,7,10,11,12$ Up to High Powers, Contemp. Math., vol. 22, Amer. Math. Soc., Providence, R.I., 1983. MR 715603 (84k:10005)
  • [3] L. E. Dickson, History of the Theory of Numbers, Chelsea, New York, 1952.
  • [4] P. Erdös, "On almost primes," Amer. Math. Monthly, v. 57, 1950, pp. 404-407. MR 0036259 (12:80i)
  • [5] P. Erdös & R. L. Graham, Old and New Problems and Results in Combinatorial Number Theory, Monographies de L'Enseignement Mathématique, No. 28, Genève, 1980.
  • [6] P. Kiss & B. M. Phong, "On a problem of A. Rotkiewicz," Math. Comp., v. 48, 1987, pp. 751-755. MR 878704 (88d:11004)
  • [7] W. L. McDaniel, "The generalized pseudoprime congruence $ {a^{n - k}} \equiv {b^{n - k}}\;\pmod n$," C. R. Math. Rep. Acad. Sci. Canada, vol. 9 (2), 1987, pp. 143-147. MR 888647 (88c:11005)
  • [8] W. L. McDaniel, "The existence of solutions of the generalized pseudoprime congruence $ {a^{f(n)}} \equiv {b^{f(n)}}\;\pmod n$." (To appear.) MR 1090649 (91k:11008)
  • [9] A. Rotkiewicz, Pseudoprime Numbers and Their Generalizations, Student Association of the Faculty of Sciences, Univ. of Novi Sad, 1972. MR 0330034 (48:8373)
  • [10] A. Rotkiewicz, "On the congruence $ {2^{n - 2}} \equiv 1\;\pmod n$," Math. Comp., v. 43, 1984, pp. 271-272. MR 744937 (85e:11005)
  • [11] M.-K. Shen, "On the congruence $ {2^{n - k}} \equiv 1\;\pmod n$," Math. Comp., v. 46, 1986, pp. 715-716. MR 829641 (87e:11005)
  • [12] M. Zhang (unpublished result).

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1989-0968152-6
Keywords: Pseudoprime
Article copyright: © Copyright 1989 American Mathematical Society

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