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

 

Fibonacci numbers that are not sums of two prime powers


Authors: Florian Luca and Pantelimon Stanica
Journal: Proc. Amer. Math. Soc. 133 (2005), 1887-1890
MSC (2000): Primary 11B39; Secondary 11B25, 11B50, 11P32
Published electronically: February 15, 2005
MathSciNet review: 2099413
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Abstract: In this paper, we construct an infinite arithmetic progression $\mathcal A$ of positive integers $n$ such that if $n\in {\mathcal A}$, then the $n$th Fibonacci number is not a sum of two prime powers.


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Additional Information

Florian Luca
Affiliation: IMATE, UNAM, Ap. Postal 61-3 (Xangari), CP. 58 089, Morelia, Michoacán, Mexico
Email: fluca@matmor.unam.mx

Pantelimon Stanica
Affiliation: Department of Mathematics, Auburn University Montgomery, Montgomery, Alabama 36124-4023
Email: pstanica@mail.aum.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07827-5
PII: S 0002-9939(05)07827-5
Keywords: Fibonacci numbers, arithmetic progressions, covering system of congruences.
Received by editor(s): February 13, 2004
Published electronically: February 15, 2005
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.