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On a conjecture of Broughan

Author(s): Santos Hernández Hernández; Florian Luca
Journal: Proc. Amer. Math. Soc. 136 (2008), 403-407.
MSC (2000): Primary 11B36; Secondary 11J68
Posted: October 24, 2007
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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:

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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