Bounds for the Solutions of Cubic Diophantine Equations

2004/10/25 by Howard Kleiman, Kleiman, Howard
Mathematics · #11 #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.NT #msc:11

paper · pdf · doi:10.48550/arxiv.math/0410519

PDF, 2pages

openalex publication_date 2004/10/25 · arxiv created 2004/11/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The original version of this paper did not take into account that there may be solutions (x₀, y_o)in Z X Z of f(x,y) = x³ + p(y)x + q(y) = 0 even though w₀ = (-3D(y₀))^(1/2) is irrational.

Related

• The diophantine equation x³/3+y³+z³-2xyz=0
• Newer sums of three cubes
• Diophantine equations with sum of cubes and cube of sum
• The Mordell-Schinzel conjecture for cubic diophantine equations
• On primitive integer solutions of the Diophantine equation x³± y³=a^k± b^k