Practical solution of the Diophantine equation $y^2 = x(x+2^ap^b)(x-2^ap^b)$

DOI10.1090/S0025-5718-06-01841-2zbMath1119.11073MaRDI QIDQ5470072

Konstantinos A. Draziotis, Dimitrios Poulakis

Publication date: 29 May 2006

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

zbMATH Keywords

Elliptic curvesCubic equationsComputer solution of Diophantine equations

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Computer solution of Diophantine equations (11Y50) Cubic and quartic Diophantine equations (11D25)

Related Items

Solving the Diophantine equation \(y^2=x(x^2 - n^2)\) ⋮ Perfect powers in elliptic divisibility sequences ⋮ On certain Diophantine equations of the form \(z^2=f(x)^2\pm g(y)^2\) ⋮ FAMILY OF ELLIPTIC CURVES <em>E^{</em>(<em>p</em>,<em>q</em>)}: <em>y</em>²=<em>x</em>²-<em>p</em>²<em>x</em>+<em>q</em>² ⋮ Integral points on the elliptic curve $y^2=x^3-4p^2x$ ⋮ INTEGRAL POINTS ON CONGRUENT NUMBER CURVES

Uses Software

• Magma
• ecdata

Cites Work

• On the practical solution of the Thue equation
• On the solution of units and index form equations in algebraic number fields
• On elliptic curves \(y^{2} = x^{3}-n^{2}x\) with rank zero
• Integral points in arithmetic progression on \(y^2= x(x^2-n^2)\)
• The Diophantine equation x⁴ - Dy² = 1, II
• The Diophantine equation $b^2X^4-dY^2=1$
• Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms
• S-integral points on elliptic curves
• Computing integral points on elliptic curves
• On the size of integer solutions of elliptic equations
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