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 language | English |
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Article number | A24 |
Pages (from-to) | 1-10 |
Number of pages | 10 |
Journal | Integers |
Volume | 21 |
State | Published - 2021 |
Scopus Subject Areas
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics