LEARNING A CLASSIFICATION OF MIXED-INTEGER QUADRATIC PROGRAMMING PROBLEMS Pierre Bonami Andrea Lodi

Source URL: cerc-datascience.polymtl.ca

Challenge Problems – Quadratics Problem 1 – Factored Form for Quadratic Equations Write a program that will accept three integer values (𝑎, 𝑟, 𝑠) as parameters for the factored form of a quadratic equation:

Source URL: bgrasley.files.wordpress.com

333 Documenta Math. Integer-Valued Quadratic Forms and Quadratic Diophantine Equations

Source URL: www.math.uiuc.edu

SMOOTH NUMBERS AND THE QUADRATIC SIEVE Carl Pomerance When faced with a large number n to factor, what do you do first? You might say “Look at the last digit,” with the idea of cheaply pulling out possible factors of

Source URL: www.mat.uniroma2.it

• Mathematics
• Integer factorization algorithms
• Number theory
• Quadratic sieve
• Special number field sieve
• Quadratic residue
• General number field sieve
• Prime number
• Lenstra elliptic curve factorization
• Sieve of Eratosthenes
• Euclidean algorithm
• Prime-counting function

Integer factorization, part 1: the Q sieve Integer factorization, part 2: detecting smoothness D. J. Bernstein

Source URL: www.mat.uniroma2.it

• Integer factorization algorithms
• Mathematics
• Number theory
• Integer sequences
• Quadratic sieve
• Discrete mathematics
• Prime number
• Smooth number
• Special number field sieve
• General number field sieve

Integer factorization, part 1: the Q sieve D. J. Bernstein Sieving small integers using primes:

Source URL: www.mat.uniroma2.it

• Mathematics
• Integer factorization algorithms
• Number theory
• Integer sequences
• Integer factorization
• Prime number
• Prime factor
• Factorization
• Quadratic sieve
• Congruence of squares

The Million-Key Question—Investigating the Origins of RSA Public Keys Petr Švenda, Matúš Nemec, Peter Sekan, Rudolf Kvašňovský, David Formánek, David Komárek, and Vashek Matyáš, Masaryk University https://www

Source URL: www.usenix.org

• Cryptography
• Integer sequences
• Integer factorization algorithms
• Primality tests
• Safe prime
• Finite fields
• RSA
• Prime number
• Strong prime
• Blum integer
• Trial division
• Quadratic sieve

Implicit Factoring: On Polynomial Time Factoring Given Only an Implicit Hint ∗ Alexander May, Maike Ritzenhofen Horst Görtz Institute for IT-security Faculty of Mathematics Ruhr-University of Bochum, 44780 Bochum, Ger

Source URL: www.cits.rub.de

• Cryptography
• Integer factorization algorithms
• Computational hardness assumptions
• E-commerce
• RSA
• Quadratic sieve
• Lattice
• Integer factorization

How Euler Did It by Ed Sandifer Odd Perfect Numbers November 2006 The subject we now call “number theory” was not a very popular one in the 18th century. Euler wrote almost a hundred papers on the subject, but the fi

Source URL: eulerarchive.maa.org

• Integer sequences
• Number theory
• Divisor function
• Algebraic number theory
• Perfect number
• Modular arithmetic
• Amicable numbers
• Divisor
• Prime number
• Quadratic reciprocity
• Leonhard Euler
• Coprime integers

APPLIED MATHEMATICAL PROGRAMMING USING ALGEBRAIC SYSTEMS by Bruce A. McCarl Professor of Agricultural Economics Texas A&M University

Source URL: agecon2.tamu.edu

• Mathematical optimization
• Operations research
• Linear programming
• Quadratic programming
• Duality
• Nonlinear programming
• Constraint
• Stochastic programming
• Integer programming
• Relaxation
• Constrained optimization
• Simplex algorithm