Solving a family of Thue equations with an application to the equation x2-Dy4=1

DOI10.4064/aa120-1-3zbMath1155.11318OpenAlexW2050449159MaRDI QIDQ3367579

Alain S. Togbé, Paul M. Voutier, Peter Gareth Walsh

Publication date: 24 January 2006

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/aa120-1-3

zbMATH Keywords

quartic Diophantine equationfamily of Thue equations

Mathematics Subject Classification ID

Thue-Mahler equations (11D59) Cubic and quartic Diophantine equations (11D25)

Related Items (15)

The number of solutions to y2=px(ax2+2) ⋮ Rational approximations to \(\root 3\of 2\) and other algebraic numbers revisited ⋮ Starting with gaps between k-free numbers ⋮ Complete solutions of the simultaneous Pell equations \((a^2+1)y^2-x^2 = y^2-bz^2 = 1\) ⋮ Simplifying method for algebraic approximation of certain algebraic numbers ⋮ Effective methods for norm-form equations ⋮ Thue's fundamental theorem. II: Further refinements and examples ⋮ Balancing and balancing-like numbers which are one away from perfect powers ⋮ A note on the Diophantine equation \(y^2=px(Ax^2+2)\) ⋮ On unit power integral bases of \(\mathbb Z[\root 4 \of {m}\)] ⋮ Integer points on the curve $Y^{2}=X^{3}\pm p^{k}X$ ⋮ The Diophantine equation aX 4 – bY 2 = 1 ⋮ A GENERALIZATION OF A THEOREM OF BUMBY ON QUARTIC DIOPHANTINE EQUATIONS ⋮ Explicit formula for the solution of simultaneous Pell equations 𝑥²-(𝑎²-1)𝑦²=1, 𝑦²-𝑏𝑧²=1 ⋮ The integral points on elliptic curves y 2 = x 3 + (36n 2 − 9)x − 2(36n 2 − 5)

This page was built for publication: Solving a family of Thue equations with an application to the equation x²-Dy⁴=1