On the Roots of the Polynomial (ab+ac+bc)x^2-(4a^2b+8abc+4a^2c)x+16a^2c

We study the polynomial (ab+ac+bc)x^2-(4a^2b+8abc+4a^2c)x+16a^2c and show its roots can be used show that Erdős–Straus Diophantine equation 4/n=1/a+1/b+1/c is true for all n.

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-04-04
DOI
https://doi.org/10.5281/zenodo.15151659
Primary Topic
Algebraic Geometry and Number Theory
Type
article
Field-Weighted Citation Impact
0.00
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article

On the Roots of the Polynomial (ab+ac+bc)x^2-(4a^2b+8abc+4a^2c)x+16a^2c

Zenodo (CERN European Organization for Nuclear Research)
Algebraic Geometry and Number Theory
article

On the Roots of the Polynomial (ab+ac+bc)x^2-(4a^2b+8abc+4a^2c)x+16a^2c

article en

Abstract

We study the polynomial (ab+ac+bc)x^2-(4a^2b+8abc+4a^2c)x+16a^2c and show its roots can be used show that Erdős–Straus Diophantine equation 4/n=1/a+1/b+1/c is true for all n.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 51%
Algebraic Geometry and Number Theory
DOIOpen Access PDFOpenAlex
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On the Roots of the Polynomial (ab+ac+bc)x^2-(4a^2b+8abc+4a^2c)x+16a^2c · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS