pell-equation

The goal of this repository is to find twin smooth integers of around 256 bits with prime sum, which can be used as public parameters in variants of the B_SIDH protocol.

Solve linear and quadratic diophantine equations in two variables: Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0

Generate the fundamental solution (minimal x) to Pell's equation for any parameter. x^2 - n*y^2 = 1

The Ramanujan street puzzle: which house numbers balance the sums on both sides? Reduces to 2m² = n(n+1).

Algoritmo de Pell em Assembly

Three barrier results for classical RSA semiprime factorization: Joux–Buchmann smoothness, Pell trace compression, and CRT walls. AI-assisted exploratory mathematics.

🔢 High-performance Rust library for solving Pell equations (x² - D·y² = 1). Features streaming API, performance boosted, arbitrary precision arithmetic, and comprehensive mathematical analysis tools. Perfect for cryptography, number theory research, and educational applications. 58 tests, zero warnings, production-ready.

Verification code for: Cofactor Dynamics and Pell Equations in GCD-Augmented Fibonacci Recurrences (DOI: 10.65737/AIRMCS2026571)

Number theory research: Lehmer-Størmer enumerator for prime-complete consecutive integer products using PARI/GP Pell equation solver

Exact record chronologies for naturally normalized energy partitions in the uncoupled two-mode oscillator spectrum, including boundary ladders, Pell-type interior records, parity effects, exact arithmetic verification, and reproducible computational tables.

Computational reproducibility companion for the Zenodo manuscript "The Pell Spine as an Optimal Rational Separator."

PROTOTYPE (v1.0). Collected volume and data deposit on consecutive powerful numbers, Pell equations, and Erdős problems #364 and #365. A reworked international version follows.