On the abc conjecture, II

2001/05/15 by C. L. Stewart, Kunrui Yu · 49 citations
Computer Science · Mathematics · #Graph Labeling and Dimension Problems #Analytic Number Theory Research #Limits and Structures in Graph Theory #Mathematics #Conjecture #abc conjecture #Combinatorics #Pure mathematics #Beal's conjecture

paper · doi:10.1215/s0012-7094-01-10815-6

published in Duke Mathematical Journal 108(1) (Duke University Press)

openalex publication_date 2001/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/13

Abstract

Let x, y, and z be coprime positive\nintegers with x+y=z. In this paper we\ngive upper bounds for z in terms of the greatest\nsquare-free factor of xyz.

Citations

• Approximate formulas for some functions of prime numbers
• On the Oesterl�-Masser conjecture
• On theabc conjecture

Cited by

• On the abc Conjecture in Algebraic Number Fields
• On the greatest prime factor of polynomial values and subexponential Szpiro in families
• Abc conjecture [wikipedia]