Tag
Quadratic Residue
6 resources tagged “Quadratic Residue” across the knowledge library.
6 items
Article7 Aug 2026Legendre, Jacobi and Kronecker Symbol ComputationThe three quadratic symbols, their differing meanings, and the reciprocity-based algorithm that computes them without factoring.2 min readRead MoreArticle7 Aug 2026Quadratic Sieve Factor Base SelectionChoosing the factor base for the quadratic sieve, the quadratic residue criterion, and the multiplier.2 min readRead MoreArticle7 Aug 2026Square Roots Modulo a Prime: the Shanks-Tonelli AlgorithmExtracting square roots modulo a prime: the easy congruence classes, the general Shanks-Tonelli algorithm, and lifting to prime powers.2 min readRead MoreArticle7 Aug 2026The Continued Fraction Factorisation MethodCFRAC: generating small quadratic residues from the continued fraction expansion, and the congruence-of-squares framework it established.2 min readRead MoreGuide6 Aug 2026Legendre, Jacobi and Kronecker SymbolsQuadratic residues, Euler's criterion, the Legendre symbol, its Jacobi and Kronecker extensions, and the reciprocity-based algorithm that evaluates them in logarithmic time.4 min readRead MoreGuide6 Aug 2026Square Roots Modulo a PrimeComputing modular square roots: the p ≡ 3 (mod 4) shortcut, the Tonelli–Shanks algorithm and its 2-adic structure, and Cornacchia's algorithm for x² + dy² = p.4 min readRead More