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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0770523-6
PII: S 0002-9939(1985)0770523-6
Article copyright: © Copyright 1985 American Mathematical Society