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Fibonacci numbers that are not sums of two prime powers

Author(s): Florian Luca; Pantelimon Stanica
Journal: Proc. Amer. Math. Soc. 133 (2005), 1887-1890.
MSC (2000): Primary 11B39; Secondary 11B25, 11B50, 11P32
Posted: February 15, 2005
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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: 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
Posted: February 15, 2005
Communicated by: David E. Rohrlich
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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