Determining the small solutions to 𝑆-unit equations

DOI10.1090/S0025-5718-99-01140-0zbMath0935.11053OpenAlexW1977969645MaRDI QIDQ4257699

Nigel P. Smart

Publication date: 31 August 1999

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-99-01140-0

zbMATH Keywords

small solutions\(S\)-unit equationsieving techniquesWildanger's method

Mathematics Subject Classification ID

Computer solution of Diophantine equations (11Y50) Exponential Diophantine equations (11D61) Multiplicative and norm form equations (11D57)

Related Items (4)

The asymptotic Fermat’s Last Theorem for five-sixths of real quadratic fields ⋮ Solving 𝑆-unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture ⋮ Computing All Elliptic Curves Over an Arbitrary Number Field with Prescribed Primes of Bad Reduction ⋮ Optimal systems of fundamental \(S\)-units for LLL-reduction

Cites Work

• Erratum. ``Solving exponential diophantine equations using lattice basis reduction algorithms
• Improved Methods for Calculating Vectors of Short Length in a Lattice, Including a Complexity Analysis
• A space efficient algorithm for group structure computation
• S -Unit Equations, Binary Forms and Curves of Genus 2
• On some computational problems in finite abelian groups
• The Solution of Triangularly Connected Decomposable Form Equations
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