Solving constrained Pell equations

DOI10.1090/S0025-5718-98-00918-1zbMath0945.11027OpenAlexW1999714276MaRDI QIDQ4383197

Kiran S. Kedlaya

Publication date: 24 March 1998

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-98-00918-1

zbMATH Keywords

Pell equationsinteger points on elliptic curvescomputer solution of diophantine equations

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Computer solution of Diophantine equations (11Y50) Cubic and quartic Diophantine equations (11D25)

Related Items (16)

Unnamed Item ⋮ Solving families of simultaneous Pell equations ⋮ On the \(D(- 1)\)-triple \(\{ 1,k^{2}+1,k^{2}+2k+2\}\) and its unique \(D(1)\)-extension ⋮ There does not exist a \(D(4)\)-sextuple ⋮ A polynomial variant of a problem of Diophantus and Euler ⋮ There are only finitely many \(D(4)\)-quintuples ⋮ Diophantine triples and construction of high-rank elliptic curves over \(\mathbb{Q}\) with three nontrivial 2-torsion points ⋮ Simultaneous quadratic equations with few or no solutions ⋮ On the size of sets in which \(xy + 4\) is always a square ⋮ Extensions of the \(D(\mp k^2)\)-triples \(\{k^2,k^2 \pm 1, 4k^2 \pm 1\}\) ⋮ Solutions of the Diophantine equation \(7X^2 + Y^7 = Z^2\) from recurrence sequences ⋮ Bounds on the number of Diophantine quintuples ⋮ The extendibility of Diophantine pairs with property $D(-1)$ ⋮ Any Diophantine quintuple contains a regular Diophantine quadruple ⋮ Diophantine \(m\)-tuples and elliptic curves ⋮ An absolute bound for the size of Diophantine \(m\)-tuples

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The simultaneous diophantine equations \(5Y^ 2-20=X^ 2\) and \(2Y^ 2+1=Z^ 2\)
• Sets in Which xy + k is Always a Square
• Simultaneous Pellian equations
• The Square Pyramid Puzzle
• THE SIMULTANEOUS DIOPHANTINE EQUATIONS y²−3x²=−2 and z²−8x²=−7
• On a Method of Solving a Class of Diophantine Equations
• Lucas and fibonacci numbers and some diophantine Equations
• Linear forms in the logarithms of algebraic numbers (IV)
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²

This page was built for publication: Solving constrained Pell equations