A note on the Erdő-Straus Conjecture

This paper makes a fundamental assertion about the Erdős-Straus conjecture. Suppose that for a prime $p$ there exists $x,y,z \in \mathbb{N}$ with $x \leq y \leq z$ so that $\frac{4}{p} = \frac{1}{x} + \frac{1}{y} + \frac{1}{z}.$ The main contribution of this paper is that, under this assumption, the Erdős-Straus conjecture can be reduced by one variable. For example, it is necessarily true that $z = \frac{xyp}{\gcd(y,p) \gcd \left( xy, x+y \right)}.$ Considering other reductions of the Erdős-Straus conjecture, this paper suggests a method for proof.

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