International Mathematical Olympiad Preliminary Selection Contest 2004 — Hong Kong Outline of Solutions Answers:

Source URL: web.hku.hk

• Integer sequences
• Integer factorization algorithms
• Prime number
• Algebraic number theory
• Field theory
• Quadratic sieve
• Wieferich prime

FACTORIZATION TECHNIQUES ELVIS NUNEZ AND CHRIS SHAW Abstract. The security of the RSA public key cryptosystem relies upon the computational difficulty of deriving the factors of a particular semiprime modulus. In this pa

Source URL: davidlowryduda.com

• Integer factorization algorithms
• Mathematics
• Cryptography
• Number theory
• Quadratic sieve
• Euclidean algorithm
• RSA
• Prime number
• Factorization
• Trial division
• General number field sieve
• Rational sieve

Fast Computation of Gauss Sums and Resolution of the Root of Unity Ambiguity Dang Khoa Nguyen Division of Mathematical Sciences School of Physical & Mathematical Sciences Nanyang Technological University

Source URL: www.ntu.edu.sg

• Polynomials
• Cyclotomic fields
• Field theory
• Algebraic numbers
• Algebraic number theory
• Gaussian period
• Quadratic Gauss sum
• Cyclotomic polynomial
• Root of unity
• Polynomial ring
• Algebraic integer
• Algebraic number field

DEPARTMENT OF MATHEMATICS UNIVERSITY OF NIJMEGEN The Netherlands Cubic reciprocity and explicit primality tests for h · 3k ± 1

Source URL: www.math.ru.nl

• Number theory
• Mathematics
• Algebra
• Algebraic number theory
• Modular arithmetic
• Quadratic residue
• Primality tests
• Integer sequences
• Reciprocity law
• Cubic reciprocity
• Prime number
• Quadratic reciprocity

Bilkent University Department of Mathematics Problem Of The Month September 2015 Problem: A real number t is said to be 10-quadratic if for some integer numbers a, b, c

Source URL: www.fen.bilkent.edu.tr

4. BINARY QUADRATIC FORMSWhat integers are represented by a given binary quadratic form?. An integer n is represented by the binary quadratic form ax2 + bxy + cy 2 if there exist integers r and s such that n = ar2

Source URL: www.dms.umontreal.ca

Explicit Primality Criteria for h #2k ± 1 Wieb Bosma Mathematics of Computation, Vol. 61, No. 203, Special Issue Dedicated to Derrick Henry Lehmer. (Jul., 1993), ppStable URL: http://links.jstor.org/sici?sici=

Source URL: www.math.ru.nl

• Mathematics
• Discrete mathematics
• Number theory
• Modular arithmetic
• Integer sequences
• Finite fields
• Quadratic residue
• Prime number
• Quadratic reciprocity
• XTR
• Coprime integers
• Factorial

Integer Factorization and Computing Discrete Logarithms in Maple Aaron Bradford∗, Michael Monagan∗, Colin Percival∗ , , Department of Mathematics, Simon Fr

Source URL: www.daemonology.net

• Cryptography
• Integer factorization algorithms
• Mathematics
• Abstract algebra
• Quadratic sieve
• General number field sieve
• Prime number
• Safe prime
• Discrete logarithm
• RSA
• Sieve of Atkin
• Quadratic residue

COMPLEX NUMBERS WITH BOUNDED PARTIAL QUOTIENTS WIEB BOSMA AND DAVID GRUENEWALD Abstract. Conjecturally, the only real algebraic numbers with bounded partial quotients in their regular continued fraction expansion are rat

Source URL: www.math.ru.nl

• Mathematics
• Mathematical analysis
• Algebraic numbers
• Continued fractions
• Number theory
• Partial fractions
• Transcendental number
• Quadratic irrational number
• Fraction
• Gaussian integer
• Partial fraction decomposition
• Pi

Noname manuscript No. (will be inserted by the editor) Extended Formulations in Mixed Integer Conic Quadratic Programming Juan Pablo Vielma, Iain Dunning, Joey Huchette and Miles

Source URL: web.mit.edu

• Operations research
• Combinatorial optimization
• Approximations
• Mathematical optimization
• Relaxation
• Linear programming relaxation
• Linear programming
• Integer programming
• Approximation algorithm
• Constructible universe