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Applications

Group theory Ring theory Knot theory Abstract algebra Computer algebra

57 related topics

Integers modulo m

§ Applications Ring M-adic integers Zero ring Empty set

16 related topics

Congruence

Integer multiple Congruence relation Equivalence relation Addition Subtraction

11 related topics

Computational complexity

Polynomial time Gaussian elimination Linear congruence theorem Montgomery reduction Discrete logarithm

10 related topics

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Overview

Motivating example

Congruence

Residue systems

Relatively prime Coprime integers

Integers modulo m

§ Applications Modular arithmetic
Ring Ring (mathematics)
M-adic integers P-adic integer
Zero ring
Empty set
Isomorphic Isomorphism
Commutative ring
Quotient ring
Ideal Ideal (ring theory)
Cyclic group
Field Field (mathematics)
Prime Prime number
Prime power
Zero-divisors Zero-divisor
Multiplicative group of the integers modulo m Multiplicative group of integers modulo n
Abelian group

Applications

Group theory
Ring theory
Knot theory
Abstract algebra
Computer algebra
Cryptography
Computer science
Chemistry
Visual Visual arts
Musical Music
International Standard Book Number
International Bank Account Numbers International Bank Account Number
CAS registry number
Check digit
Public key Public-key cryptography
RSA RSA (algorithm)
Diffie–Hellman Diffie–Hellman key exchange
Finite fields Finite field
Elliptic curves Elliptic curve
Symmetric key algorithms Symmetric key algorithm
Advanced Encryption Standard
International Data Encryption Algorithm
RC4
Modular exponentiation
Polynomial factorization
Polynomial greatest common divisor
Linear algebra
Gröbner basis
Fidonet
Rosetta Code

Computational complexity

Polynomial time
Gaussian elimination
Linear congruence theorem
Montgomery reduction
Discrete logarithm
Quadratic congruence Quadratic congruences
Integer factorization
Encryption
NP-intermediate
NP-complete

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Modular arithmetic

Nodes129

Edges128

Triples45

Avg. degree1.98

Density0.015504

Components1

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Modular arithmetic

Top relations

see also · 11

Modular arithmetic → Boolean, Carmichael's, Cyclic, Euler's, Fibonacci, Finite, Lagrange's, Multiplicative, Primitive, Reduced, Two-element Boolean

has application · 8

Modular arithmetic → CAS, For, IBANs, In, International Bank Account Numbers, International Standard Book Number, ISBN, Likewise

related to External links · 8

Modular arithmetic → An, Arithmetic, Congruence, EMS Press, Encyclopedia, GIMPS, In, Mathematics

related to Computational complexity · 7

Modular arithmetic → Algorithms, Gaussian, Montgomery, NP-intermediate, Since, Some, These

related to Motivating example · 6

Modular arithmetic → After, If, Ordinary, Similarly, This, We

is a · 2

Modular arithmetic → hour hand on a 12-hour clock, system of arithmetic operations for integers

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Important terminology

modulo mod arithmetic modular integer residue congruence integers displaystyle system coprime used number ring prime remainder one mathbb division euler's

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Modular arithmetic	is a	system of arithmetic operations for integers	0.90	text
Modular arithmetic	is a	hour hand on a 12-hour clock	0.90	text
RSA	instance of	modular arithmetic directly underpins public key systems	0.80	text
Diffie	instance of	modular arithmetic directly underpins public key systems	0.80	text
politics	instance of	modular arithmetic also has application in disciplines	0.80	text
Modular arithmetic	has application	In	0.60	section
Modular arithmetic	has application	For	0.60	section
Modular arithmetic	has application	International Standard Book Number	0.60	section
Modular arithmetic	has application	ISBN	0.60	section
Modular arithmetic	has application	Likewise	0.60	section
Modular arithmetic	has application	International Bank Account Numbers	0.60	section
Modular arithmetic	has application	IBANs	0.60	section

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Applications

Integers modulo m

Congruence

Computational complexity

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Overview

Motivating example

Congruence

Basic properties

Advanced properties

Congruence classes

Residue systems

Integers modulo m

Applications

Computational complexity

Advanced semantic analysis

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Modular arithmetic

How this topic connects Entity context

Modular arithmetic

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges