Number Theory


The Chameleon Effect, the Binomial Theorem and Beal's Conjecture

Authors: Julian Beauchamp

In psychology, the Chameleon Effect describes how an animal's behaviour can adapt to, or mimic, its environment through non-conscious mimicry. In the first part of this paper, we show how $a^x - b^y$ can be expressed as a binomial expansion (with an upper index, $z$) that, like a chameleon, mimics a standard binomial formula (to the power $z$) without its own value changing even when $z$ itself changes. In the second part we will show how this leads to a proof for the Beal Conjecture. We finish by outlining how this method can be applied to a more generalised form of the equation.

Comments: 9 Pages.

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Submission history

[v1] 2017-12-29 15:51:45

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