A note on the erdős-straus conjecture

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Abstract

This paper makes a fundamental assertion about the Erdős-Straus conjecture. Sup-pose that for a prime p there exists x, y, z ∈ N with x ≤ y ≤ z so that 4 p= 1x+ 1y+ 1z. 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 xyp z = gcd(y, p) gcd (xy, x + y). Considering other reductions of the Erdős-Straus conjecture, this paper suggests a method for proof.

Original languageEnglish
Article numberA24
Pages (from-to)1-10
Number of pages10
JournalIntegers
Volume21
StatePublished - 2021

Scopus Subject Areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics

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