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On a conjecture of Broughan

Authors: Santos Hernández Hernández and Florian Luca
Journal: Proc. Amer. Math. Soc. 136 (2008), 403-407
MSC (2000): Primary 11B36; Secondary 11J68
Published electronically: October 24, 2007
MathSciNet review: 2358477
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Abstract: In this paper, we confirm a conjecture of Broughan, concerning the closure of the set of Fibonacci numbers in the full topology over $ \mathbb{Z}$.

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

  • 1. M. Aigner and G. M. Ziegler, Proofs from The Book, Springer-Verlag, 1998.
  • 2. K.  A.  Broughan, `Adic Topologies for the Rational Integers' Canad. J. Math. 55 (2003), 711-723. MR 1994070 (2004i:11005)
  • 3. H. Fürstenberg, `On the infinitude of primes', Amer. Math. Monthly 62 (1955), 353. MR 0068566 (16:904e)
  • 4. S.  Hernández and F. Luca, `Common Factors of Shifted Fibonacci Numbers', Per. Math. Hungarica 47 (2003), 95-110. MR 2024976 (2004h:11017)
  • 5. T. Koshy, Fibonacci and Lucas numbers with applications, Pure and Applied Mathematics (New York). Wiley-Interscience, New York, 2001. MR 1855020 (2002f:11015)

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Additional Information

Santos Hernández Hernández
Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago, Chile

Florian Luca
Affiliation: Instituto de Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, México

Received by editor(s): May 2, 2006
Received by editor(s) in revised form: August 15, 2006
Published electronically: October 24, 2007
Communicated by: Ken Ono
Article copyright: © Copyright 2007 American Mathematical Society

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