Journal of Formalized Mathematics
Volume 14, 2002
University of Bialystok
Copyright (c) 2002 Association of Mizar Users

## Fibonacci Numbers

Robert M. Solovay
P. O. Box 5949, Eugene OR 97405, U. S. A.

### Summary.

We show that Fibonacci commutes with g.c.d.; we then derive the formula connecting the Fibonacci sequence with the roots of the polynomial $x^2 - x - 1.$

#### MML Identifier: FIB_NUM

The terminology and notation used in this paper have been introduced in the following articles [2] [9] [10] [5] [1] [3] [4] [7] [6] [8]

#### Contents (PDF format)

1. Fibonacci Commutes with gcd
2. Fibonacci Numbers and the Golden Mean

#### Acknowledgments

My thanks to Freek Wiedijk for helping me learn Mizar and to Piotr Rudnicki for instructive comments on an earlier version of this article. This article was finished while I was visiting Bialystok and Adam Naumowicz and Josef Urban helped me through some difficult moments.

#### Bibliography

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