Engineering↗
Legendre, Jacobi and Kronecker Symbol Computation
The three quadratic symbols, their differing meanings, and the reciprocity-based algorithm that computes them without factoring.
Tag
Quadratic Residue
Every page in the KEVOS library tagged Quadratic Residue. 6 pages.
Engineering↗
Quadratic Sieve Factor Base Selection
Choosing the factor base for the quadratic sieve, the quadratic residue criterion, and the multiplier.
Engineering↗
Square Roots Modulo a Prime: the Shanks-Tonelli Algorithm
Extracting square roots modulo a prime: the easy congruence classes, the general Shanks-Tonelli algorithm, and lifting to prime powers.
Engineering↗
The Continued Fraction Factorisation Method
CFRAC: generating small quadratic residues from the continued fraction expansion, and the congruence-of-squares framework it established.
Engineering↗
Legendre, Jacobi and Kronecker Symbols
Quadratic residues, Euler's criterion, the Legendre symbol, its Jacobi and Kronecker extensions, and the reciprocity-based algorithm that evaluates them in logarithmic time.
Engineering↗
Square Roots Modulo a Prime
Computing 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.
Related
Other tags in the library.
mathematics 387
abstract algebra 252
Machine Design 184
business 179
project management 158
Computational Number Theory 123
algebra handbook 85
graduate mathematics 85
handbook 79
templates and examples 78
History of Engineering 77
Manufacturing 76
algebra and trigonometry 74
universal algebra 62
algebra 60
project delivery 60
principles of project management 58
advanced algebra 53
Fasteners and Joints 53
Civil Engineering 48
CAD 42
Context and scope 42
Machine Elements 40
Threading and Gaging 37
Mechanical Engineering 35
Power Transmission 34
template 34
Operational Excellence 32
example 31
project leadership 31
project teams 31
strategy 31
Business Expansion 29
Metrology 29
project management research 29
Sales & Marketing 29
personal development 27
behaviour change 26
habits 26
systems 26