Hi all, I found the following statement on a magazine page and cannot understand it. It is possibly very distant from the little maths I know, but made me very curious.(adsbygoogle = window.adsbygoogle || []).push({});

It is therein said that if a number $$n$$ is a Fibonacci number, then one of the conditions $$ 5n^2 + 4$$ or $$5n^2-4$$ is true.

The conclusion follows from the following relationship, where $$A_n$$ is the n-th number in the Fibonacci sequence.

$$n = log_{golden ratio} \frac{A_n \sqrt{5} + \sqrt{5A_n^2 +-4}}{2}$$.

I am unable to see how the conclusion is drawn, any hint would be most appreciated.

Thanks a lot

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Condition for a number to be a Fibonacci one

Loading...

Similar Threads for Condition number Fibonacci |
---|

A Last Gauss Lemma Section II |

A Reality conditions on representations of classical groups |

B Why does every subfield of Complex number have a copy of Q? |

**Physics Forums | Science Articles, Homework Help, Discussion**