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On a problem of A. Rotkiewicz


Authors: P├ęter Kiss and Bui Minh Phong
Journal: Math. Comp. 48 (1987), 751-755
MSC: Primary 11A51; Secondary 11A05
DOI: https://doi.org/10.1090/S0025-5718-1987-0878704-8
MathSciNet review: 878704
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Abstract | References | Similar Articles | Additional Information

Abstract: For any fixed positive integers a, $ k \geqslant 2$ there are infinitely many composite integers n such that $ {a^{n - k}} \equiv 1\;(\bmod n)$.


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

  • [1] G. D. Birkhoff & H. S. Vandiver, "On the integral divisors of $ {a^n} - {b^n}$," Ann. of Math. (2), v. 5, 1904, pp. 173-180. MR 1503541
  • [2] A. Makowski, "Generalization of Morrow's D numbers," Simon Stevin, v. 36, 1962, p. 71. MR 0146136 (26:3662)
  • [3] D. C. Morrow, "Some properties of D numbers," Amer. Math. Monthly, v. 58, 1951, pp. 329-330. MR 1527863
  • [4] D. S. Mitrinović & M. S. Popadić, Inequalities in Number Theory, Naucni Podmladak, Univ. of Niš, 1978, 183 pp. MR 525579 (80c:10002)
  • [5] A. Rotkiewicz, Pseudoprime Numbers and Their Generalizations, Student Assoc. of the Faculty of Sci., Univ. of Novi Sad, 1972, 169 pp. MR 0330034 (48:8373)
  • [6] A. Rotkiewicz, "On the congruence $ {2^{n - 2}} \equiv 1\;\pmod n$," Math. Comp., v. 43, 1984, pp. 271-272. MR 744937 (85e:11005)
  • [7] K. Zsigmondy, "Zur Theorie der Potenzreste," Monatsh. Math., v. 3, 1892, pp. 265-284. MR 1546236

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1987-0878704-8
Keywords: Congruence, primitive prime divisor
Article copyright: © Copyright 1987 American Mathematical Society

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