Number Theory

Number Theory#

The Theory of Integers

Sections#

Resources#

My Lesson

  • [ y ] 07-29-2021. “Number Theory and Cryptography Complete Course | Discrete Mathematics for Computer Science”.

Richard E. Borcherds

  • [ y ] 01-13-2022. “Introduction to number theory lecture 1.”.

  • [ y ] 01-15-2022. “Introduction to number theory lecture 2: Survey.”.

  • [ y ] 01-17-2022. “Introduction to number theory lecture 3: Divisibility and Euclid’s algorithms.”.

  • [ y ] 01-18-2022. “Introduction to number theory lecture 4. More on Euclid’s algorithm”.

  • [ y ] 01-20-2022. “Introduction to number theory lecture 5. Primes.”.

more

  • [ y ] 11-13-2023. Douglas Shamlin Jr. “Ultimate Large Numbers List 2024 - The Biggest Numbers Ever!!!”.

  • [ y ] 11-21-2023. Shefs of Problem Solving. “A number theory adventure - JBMO 2002 - P3”.

[ y ] 02-28-2019 Shannon “MATHCHICK” Myers. “Direct Proof and Counterexample V: Floor and Ceiling”.

[ h ] The PrimePages: prime number research & records

https://2π.com/09/12/integer-factorization-in-64-bit/

Texts#

Bressoud. Factorization and Primality Testing. Springer.

Crandall & Pomerance. Prime Numbers: A Computational Perspective. Springer.

Davenport. The Higher Arithmetic. CUP.

LeVeque. Fundamentals of Number Theory. Dover.

[ h ] Vaughan, Robert. A Course of Elementary Number Theory.

Wagstaff. The Joy of Factoring. American Mathematical Society.

Figures#

  • [ w ] 1730-1783 Bézout, Étienne

  • [ w ] 1950----- Bressoud, David

  • [ w ] 1879-1967 Carmichael, Robert

  • [ w ] 1947----- Cohen, Henri

  • [ w ] 1947-2012 Crandall, Richard

  • [ w ] 1865-1963 Hadamard, Jacques

  • [ w ] 1877-1947 Hardy, G. H.

  • [ w ] --------- Lehman, R. Sherman

  • [ w ] 1842-1891 Lucas, Édouard

  • [ w ] 1944----- Pomerance, Carl

  • [ w ] 1866-1962 Poussin, Charles Jean de la Vallée

  • [ w ] 1948----- Schroeppel, Richard

  • [ w ] 1945----- Vaughan, Robert

  • [ w ] 1945----- Wagstaff Jr., Samuel S.

Terms#

  • [ w ] Aliquot Sum

  • [ w ] Arbitrary-Precision Arithmetic

  • [ w ] Arithmetic Function

  • [ w ] Bézout’s Identity

  • [ w ] Binary GCD Algorithm

  • [ w ] Carmichael Number

  • [ w ] Chinese Remainder Theorem

  • [ w ] Computational Number Theory

  • [ w ] Congruence of Squares

  • [ w ] Congruence Relation

  • [ w ] Coprime

  • [ w ] Diophantine Equation

  • [ w ] Dixon’s Factorization Method

  • [ w ] Euclid’s Lemma

  • [ w ] Euclid’s Theorem

  • [ w ] Euclidean Algorithm

  • [ w ] Euler’s Criterion

  • [ w ] Euler’s Totient Function

  • [ w ] Extended Euclidean Algorithm

  • [ w ] Factor Base

  • [ w ] Fast Inverse Square Root

  • [ w ] Fast Library for Number Theory (FLINT)

  • [ w ] Fermat Number

  • [ w ] Fermat’s Little Theorem

  • [ w ] Fermat’s Factorization Method

  • [ w ] Fundamental Theorem of Arithmetic

  • [ w ] General Number Field Sieve

  • [ w ] Greatest Common Divisior (GCD)

  • [ w ] GNU Multiple Precision Arithmetic Library (GMP)

  • [ w ] Integer Factorization

  • [ w ] Integer Square Root

  • [ w ] Jacobi Symbol

  • [ w ] L-Notation

  • [ w ] Law of Quadratic Reciprocity

  • [ w ] Law of Quadratic Reciprocity, proofs

  • [ w ] Legendre Symbol

  • [ w ] Lehmer’s GCD Algorithm

  • [ w ] Linnik’s Theorem

  • [ w ] Lucas’ Theorem

  • [ w ] Modular Arithmetic

  • [ w ] Number Theory Library

  • [ w ] PARI/GP

  • [ w ] Pollard’s Rho Algorithm

  • [ w ] Primality Test

  • [ w ] Prime Gap

  • [ w ] Prime Number Theorem

  • [ w ] Prime Power

  • [ w ] Prime, lists

  • [ w ] Prime-Counting Function

  • [ w ] Quadratic Residue

  • [ w ] Quadratic Sieve

  • [ w ] Rational Sieve

  • [ w ] Reduced Residue System

  • [ w ] Residue Number System

  • [ w ] RSA (Rivest–Shamir–Adleman)

  • [ w ] Sieve Theory

  • [ w ] Special Number Field Sieve

  • [ w ] Square Number

  • [ w ] Square Root, methods of computing

  • [ w ] Totativie

  • [ w ] Trial Division

  • [ w ] Wheel Factorization

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