The Diophantine equation aX 4 – bY 2 = 1
From MaRDI portal
Publication:3631297
DOI10.1515/CRELLE.2009.034zbMath1185.11017arXiv0903.1742OpenAlexW2963619908MaRDI QIDQ3631297
Publication date: 5 June 2009
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0903.1742
Cubic and quartic Diophantine equations (11D25) Higher degree equations; Fermat's equation (11D41) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)
Related Items (5)
The number of solutions to y2=px(ax2+2) ⋮ Complete solutions of the simultaneous Pell equations \((a^2+1)y^2-x^2 = y^2-bz^2 = 1\) ⋮ On the Diophantine equation \(X^2 - (1 + a^2)Y^4 = - 2a\) ⋮ On the Diophantine equation \(X^2-(p^{2m}+1)Y^6=-p^{2m}\) ⋮ On the solvability of the simultaneous Pell equations x2 − ay2 = 1 and y2 − bz2 = v12
Cites Work
- Complete solution of the diophantine equation \(X^ 2+1=dY^ 4\) and a related family of quartic Thue equations
- On the method of Thue-Siegel
- On the representation of integers by binary cubic forms of positive discriminant
- On a family of quartic Thue inequalities. I
- Cubic Thue inequalities with negative discriminant.
- On the representation of unity by binary cubic forms
- Solving a family of Thue equations with an application to the equation x2-Dy4=1
- The Diophantine equation $b^2X^4-dY^2=1$
- A GENERALIZATION OF A THEOREM OF BUMBY ON QUARTIC DIOPHANTINE EQUATIONS
- Some Remarks on the Diophantine Equations x 2 − Dy 4 = 1 and x 4 − Dy 2 = 1
- On the Diophantine Equation mX 2 - nY 2 = ± 1
This page was built for publication: The Diophantine equation aX 4 – bY 2 = 1
