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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
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] Richard K. Guy, Unsolved problems in number theory, Unsolved Problems in Intuitive Mathematics, vol. 1, Springer-Verlag, New York-Berlin, 1981. Problem Books in Mathematics. MR 656313
  • [2] Daniel Shanks, Solved and unsolved problems in number theory. Vol. I, Spartan Books, Washington, D.C., 1962. MR 0160741

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