Section 48.1 Introduction
For my final project I am researching the accessibility of Fibonacci numbers. Particularly, I want to find the degree of accessibility of the Fibonacci set denoted as \(F\text{.}\) It is proven that the degree of accessibility is at most 5. [14.7.3.2]
Another paper, [48.7.2], focuses on finding the degree of accessibility of even Fibonacci numbers, amongst other topics including super–accessibility which I will not elaborate on in this report. The paper provides a proof that the even Fibonacci numbers is at most 2–accessible and as a corollary this proves that the degree of accessibility for the Fibonacci numbers is at most \(5\text{,}\) which agrees with the first paper's conclusion. Additionally the paper creates a conjecture that the even Fibonacci numbers are not 2–accessible, and is reinforced with computer results.
My goal for this project is to prove that the even Fibonacci numbers are 2–accessible or the converse. Unfortunately I have been unable to do this in the past 4 months. I have discovered that a family of sets are accessible and proved Euler's theorem using this family of sets. So this report is both a compilation of proofs about the accessibility of even Fibonacci numbers by the mentioned papers, and my own proof.