The Solution of Triangularly Connected Decomposable Form Equations

DOI10.2307/2153453zbMath0831.11027OpenAlexW2028270314MaRDI QIDQ4846022

Nigel P. Smart

Publication date: 18 February 1996

Full work available at URL: https://doi.org/10.2307/2153453

zbMATH Keywords

sieveWeierstrass points\(S\)-unit equationcurves of genus 2\(p\)-adic reduction stepcomplex reduction steptriangularly connected decomposable form equationstriangularly connected linear forms

Mathematics Subject Classification ID

Computer solution of Diophantine equations (11Y50) Higher degree equations; Fermat's equation (11D41)

Related Items (13)

Determining the small solutions to 𝑆-unit equations ⋮ Solving norm form equations via lattice basis reduction ⋮ AN APPLICATION OF THE MODULAR METHOD AND THE SYMPLECTIC ARGUMENT TO A LEBESGUE–NAGELL EQUATION ⋮ Finitely generated sets of fuzzy values: if ``and is exact, then ``or is almost always approximate, and vice versa -- a theorem ⋮ On the solutions of the Diophantine equation \((x-d)^2 +x^2 +(x+d)^2 =y^n\) for \(d\) a prime power ⋮ Exceptional units in a family of quartic number fields ⋮ On the resolution of relative Thue equations ⋮ Computing All Elliptic Curves Over an Arbitrary Number Field with Prescribed Primes of Bad Reduction ⋮ Optimal systems of fundamental \(S\)-units for LLL-reduction ⋮ Solving Thue equations without the full unit group ⋮ Sums of exceptional units in residue class rings ⋮ On the solution of units and index form equations in algebraic number fields ⋮ Non-monogeneity in a family of sextic fields

Uses Software

• KANT/KASH

Cites Work

• Solving exponential diophantine equations using lattice basis reduction algorithms
• On the resolution of index form equations in biquadratic number fields. I
• On the resolution of index form equations in biquadratic number fields. II
• On the practical solution of the Thue equation
• On the number of solutions of linear equations in units of an algebraic number field
• Factoring polynomials with rational coefficients
• Logarithmic forms and group varieties.
• Linear forms in p-adic logarithms
• Matrix Analysis
• Products of Prime Powers in Binary Recurrence Sequences Part I: The Hyperbolic Case, with an Application to the Generalized Ramanujan-Nagell Equation
• Computing All Power Integral Bases of Cubic Fields
• Elliptic Curves of Conductor 11
• Solving a Specific Thue-Mahler Equation
• A hyperelliptic diophantine equation related to imaginary quadratic number fields with class number 2.
• On the greatest prime factors of decomposable forms at integer points
• Explicit upper bounds for the solutions of some diophantine equations
• Curves of genus 2 with good reduction away from 2 with a rational Weierstrass point
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