Geodesic
Trigonometric expressions for Fibonacci and Lucas numbers
Acta mathematica Universitatis Comenianae, Tome 79 (2010) no. 2 
B. Sury. Trigonometric expressions for Fibonacci and Lucas numbers. Acta mathematica Universitatis Comenianae, Tome 79 (2010) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2010_79_2_a4/
@article{AMUC_2010_79_2_a4,
     author = {B. Sury},
     title = {Trigonometric expressions for {Fibonacci} and {Lucas} numbers},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2010},
     volume = {79},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2010_79_2_a4/}
}
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Voir la notice de l'article provenant de la source Comenius University

The amount of literature bears witness to the ubiquity of the Fibonacci numbers and the Lucas numbers. Not only are these numbers popular in expository literature because of their beautiful properties, but also the fact that they `occur in nature' adds to their fascination. Our purpose is to use a certain polynomial identity to express these numbers in terms of trigonometric functions. It is interesting that these expressions provide natural proofs of old and new divisibility properties for the Fibonacci numbers. One can recover naturally some divisibility properties and discover/observe some others which seem to be new. There are some fascinating open questions about the periodicity of the Fibonacci sequences modulo primes and we shall also prove some partial results on this. <br><B>Keywords</b>:&nbsp; moduls of a measure; <FONT SIZE='3' FACE='Symbol'>&#116;</FONT>-smooth and tight vector measures. &nbsp;