Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-07-08875-2
Published electronically: October 24, 2007
MathSciNet review: 2358477
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11B36, 11J68

Retrieve articles in all journals with MSC (2000): 11B36, 11J68


Additional Information

Santos Hernández Hernández
Affiliation: Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago, Chile
Email: shernand@mat.puc.cl

Florian Luca
Affiliation: Instituto de Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, México
Email: fluca@matmor.unam.mx

DOI: https://doi.org/10.1090/S0002-9939-07-08875-2
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

American Mathematical Society