On the Computational Complexity of Determining the Solvability or Unsolvability of the Equation X 2 - DY 2 = -1
From MaRDI portal
Publication:3890763
DOI10.2307/1998017zbMath0446.10014OpenAlexW4249765387MaRDI QIDQ3890763
Publication date: 1980
Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/1998017
Analysis of algorithms and problem complexity (68Q25) Quadratic and bilinear Diophantine equations (11D09) Complexity of computation (including implicit computational complexity) (03D15) Algorithms in computer science (68W99) General binary quadratic forms (11E16)
Related Items (19)
On similarity classes of second order matrices with zero trace over the ring of integers ⋮ Effective estimates on integral quadratic forms: Masser's conjecture, generators of orthogonal groups, and bounds in reduction theory ⋮ Quadratic forms in models of \(I\Delta _{0}+\Omega _{1}\). I ⋮ InfoMod: a visual and computational approach to Gauss' binary quadratic forms ⋮ Dirichlet’s proof of the three-square theorem: An algorithmic perspective ⋮ Compact representation of quadratic integers and integer points on some elliptic curves ⋮ Density computations for real quadratic units ⋮ Bounds for the smallest integral point on a conic over a number field ⋮ On the computation of quadratic 2-class groups ⋮ Mixed-integer quadratic programming is in NP ⋮ Relative norm of the fundamental unit of certain biquadratic fields and parity of the lengths of cycles of reduced ideals ⋮ All Functions $$g: \mathbb{N} \rightarrow \mathbb{N}$$ Which have a Single-Fold Diophantine Representation are Dominated by a Limit-Computable Function $$f: \mathbb{N}\setminus \{0\} \rightarrow \mathbb{N}$$ Which is Implemented in MuPAD and Whose Computability is an Open Problem ⋮ Characterization of regular Diophantine quadruples ⋮ On the evolution of continued fractions in a fixed quadratic field ⋮ Minimizing Cubic and Homogeneous Polynomials over Integers in the Plane ⋮ Sylow subgroups of ideal class groups with moduli ⋮ Uniformly Diophantine numbers in a fixed real quadratic field ⋮ The negative Pell equation and Pythagorean triples ⋮ Complexity questions in number theory
This page was built for publication: On the Computational Complexity of Determining the Solvability or Unsolvability of the Equation X 2 - DY 2 = -1
