The Euclidean Algorithm and a Generalization of the Fibonacci Sequence
نویسنده
چکیده
This paper will explore the relationship between the Fibonacci numbers and the Euclidean Algorithm in addition to generating a generalization of the Fibonacci Numbers. It will also look at the ratio of adjacent Fibonacci numbers and adjacent generalized Fibonacci numbers. Finally it will explore some fun applications and properties of the Fibonacci numbers.
منابع مشابه
A Generalized Fibonacci Sequence and the Diophantine Equations $x^2pm kxy-y^2pm x=0$
In this paper some properties of a generalization of Fibonacci sequence are investigated. Then we solve the Diophantine equations $x^2pmkxy-y^2pm x=0$, where $k$ is positive integer, and describe the structure of solutions.
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