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Everything about Modular arithmetic
Computation modulo a fixed integer
In mathematics, modular arithmetic is a system of arithmetic operations for integers, differing from the usual ones in that numbers "wrap around" when reaching or exceeding a certain value, called the modulus. The modern approach to number theory using modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Modular arithmeticA 5-minute orientation
- Skim a recent paper: An improved QFT-based quantum comparator and extended modular arithmetic using one ancilla qubitInfluential work since 2022
- Pick up a classic book: Finite mathematics and its applicationsThe most-reprinted book on the subject
- Read the landmark paper: Efficient Word Size Modular ArithmeticCited 52 times
- Go sideways: Modular multiplicative inverseA closely related topic
- Go sideways: Multiplicative group of integers modulo nA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Efficient Word Size Modular Arithmetic
Incomplete reduction in modular arithmetic
Analysis of modular arithmetic
Semi-Arithmetic Fuchsian Groups and Modular Embeddings
Fast Parallel Arithmetic via Modular Representation
Fast Integer Multiplication Using Modular Arithmetic
Arithmetic statistics of modular symbols
ARITHMETIC TRACES OF NON-HOLOMORPHIC MODULAR INVARIANTS
🆕 Influential since 2022
An improved QFT-based quantum comparator and extended modular arithmetic using one ancilla qubit
A selective image encryption algorithm based on a chaotic model using modular sine arithmetic
Secret image sharing by using multi-prime modular arithmetic
AMBTC-based secret image sharing by simple modular arithmetic
TransModE: Translational Knowledge Graph Embedding Using Modular Arithmetic
📚 Books worth reading
Finite mathematics and its applicationsLarry Joel Goldstein, David I. Schneider · 1969
Finite mathematicsMargaret L. Lial · 1977
Finite mathematics and calculus with applicationsMargaret L. Lial · 1970
Representation theory of finite groups and associative algebrasCharles W. Curtis · 1962
Some applications of modular formsPeter Sarnak · 1990- 📕Analysis and Control of Finite-Valued SystemsHaitao Li, Guodong Zhao · 2018
Residue arithmetic and its applications to computer technologyNicholas S. Szabó · 1967- 📕Existence of smalll zero-sum subsets of large sets of residue classesDale E. Green · 1989
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Modular multiplicative inverse In mathematics, particularly in the area of arithmetic, a modular multiplicative inverse of an integer a is an integer x such that the product ax is congruent…
- Multiplicative group of integers modulo n In modular arithmetic, the integers coprime (relatively prime) to n from the set {0,1,…,n−1} of n non-negative integers form a group under multiplication…
- Euler's theorem In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that, if n and a are coprime positive integers…
- Primitive root modulo n In number theory, a number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n. In symbols, g is a primitive…
- Fermat's little theorem In number theory, Fermat's little theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p. In…
- Multiplicative order In number theory, given a positive integer n and an integer a coprime to n, the multiplicative order of a modulo n is the smallest positive integer k such…
- Reduced residue system In mathematics, a subset R of the integers is called a reduced residue system modulo n if: gcd(r, n) = 1 for each r in R, R contains φ(n) elements, no…
- Montgomery modular multiplication In modular arithmetic computation, Montgomery modular multiplication, more commonly referred to as Montgomery multiplication, is a method for performing…