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Pairs where $ 2\sp a-2\sp b$ divides $ n\sp a-n\sp b$ for all $ n$


Authors: Qi Sun and Ming Zhi Zhang
Journal: Proc. Amer. Math. Soc. 93 (1985), 218-220
MSC: Primary 11A07
DOI: https://doi.org/10.1090/S0002-9939-1985-0770523-6
MathSciNet review: 770523
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Abstract: Recently Selfridge asked for what $ a$ and $ b$ does $ {2^a} - {2^b}$ divide $ {n^a} - {n^b}$ for all $ n$? In this paper, the authors prove that there exist only fourteen such pairs $ (a,b)$ when $ 0 \leq b < a$.


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

  • [1] R. K. Guy, Unsolved problems in number theory, Springer-Verlag, New York, 1981, p. 57. MR 656313 (83k:10002)
  • [2] D. Shanks, Solved and unsolved problems in number theory, Vol. 1, Spartan, Washington, D.C., 1962, p. 120. MR 0160741 (28:3952)

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DOI: https://doi.org/10.1090/S0002-9939-1985-0770523-6
Article copyright: © Copyright 1985 American Mathematical Society

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