Approximate equality for two sums of roots

DOI10.1016/J.JCO.2024.101866MaRDI QIDQ6564670

A. Dubickas

Publication date: 1 July 2024

Published in: Journal of Complexity (Search for Journal in Brave)

zbMATH Keywords

approximationLiouville theorem\textit{abc}-conjecturesquare root sum problem

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17) Distribution modulo one (11J71) Approximation to algebraic numbers (11J68)

Cites Work

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• On the minimum gap between sums of square roots of small integers
• How much precision is needed to compare two sums of square roots of integers?
• Diophantine equations \(x^ m-Ay^ n=k\)
• Diophantine equation \(x^3-y^2=k\) and Hall's conjecture
• Letter to the editor: Diophantine equation \(x^ 3-y^ 2=k\) and Hall's conjecture
• A strong and easily computable separation bound for arithmetic expressions involving radicals
• Neighboring powers
• Search for good examples of Hall’s conjecture
• Effective estimates of solutions of some diophantine equations
• Bounding the sum of square roots via lattice reduction
• Minimal gaps and additive energy in real-valued sequences
• USSR is in P/poly

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