On representations by Egyptian fractions
Florin Ambro, Mugurel Barcau
TL;DR
This paper establishes a precise upper limit for the size of the terms in Egyptian fraction representations of rational numbers, advancing understanding of their structure.
Contribution
It provides a sharp upper bound on the entries of Egyptian fraction representations, a novel theoretical result in number theory.
Findings
Derived a tight upper bound for Egyptian fraction entries
Improved understanding of the structure of Egyptian fractions
Potential applications in number theory and algorithms
Abstract
We give a sharp upper bound for the entries of the representations of a rational number as a sum of Egyptian fractions.
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Identities · Algebraic Geometry and Number Theory