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Word with multiple distinct meanings
In mathematics, the term modulo ("with respect to a modulus of", the Latin ablative of modulus which itself means "a small measure") is often used to assert
Modulo_(mathematics)
Computation modulo a fixed integer
buffer Division (mathematics) Finite field Legendre symbol Modular exponentiation Modulo (mathematics) Multiplicative group of integers modulo n Pisano period
Modular_arithmetic
Computational operation
In computing and mathematics, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, the
Modulo
Topics referred to by the same term
Modulus (digital counter), the number of states in a counter's count sequence Modulo operation (a % b, mod(a, b), etc.), in both math and programming languages;
Modulus
Modular arithmetic concept
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 root modulo n if for every
Primitive_root_modulo_n
denotes the congruence modulo an integer. 3. May denote a logical equivalence. ≅ 1. May denote an isomorphism between two mathematical structures, and is
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Property of being an even or odd number
commutative and associative in modulo 2 arithmetic, and multiplication is distributive over addition. However, subtraction in modulo 2 is identical to addition
Parity_(mathematics)
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Group of units of the ring of integers modulo n
non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n. Equivalently, the elements of this group can
Multiplicative group of integers modulo n
Multiplicative_group_of_integers_modulo_n
Natural number
reduction modulo 2 records the parity of an integer: even integers are congruent to 0 modulo 2, and odd integers are congruent to 1 modulo 2. In algebra
2
Topics referred to by the same term
partitioning attack applicable to block and stream ciphers Modulo (mathematics) Modular arithmetic Modulo operation Modular exponentiation MOD., a science museum
Mod
Algorithmic runtime requirements for common math procedures
1090/S0025-5718-07-02017-0. Bernstein, D.J. "Faster Algorithms to Find Non-squares Modulo Worst-case Integers". Brent, Richard P.; Zimmermann, Paul (2010). "An O
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
Integer that is a perfect square modulo some integer
number theory, an integer q is a quadratic residue modulo n if it is congruent to a perfect square modulo n; that is, if there exists an integer x such that
Quadratic_residue
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or
List of mathematical constants
List_of_mathematical_constants
Topics referred to by the same term
a remainder as result. Modulo may also refer to: Modulo (mathematics), a word with multiple distinct meanings in mathematics Modular arithmetic, a part
Modulo_(disambiguation)
Arithmetic operation
division, or by faster methods; see Division algorithm. In modular arithmetic (modulo a prime number) and for real numbers, nonzero numbers have a multiplicative
Division_(mathematics)
Natural number
{\displaystyle n} + 1 are greater than 1 so their product is not prime. The integers modulo 3 form the finite field F 3 {\displaystyle \mathbb {F} _{3}} , the smallest
3
Logical problem studied in computer science
computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable
Satisfiability modulo theories
Satisfiability_modulo_theories
Fundamental trigonometric functions
advantage and efficiency advantage for computing modulo to one period. Computing modulo 1 turn or modulo 2 half-turns can be losslessly and efficiently
Sine_and_cosine
In mathematics, invertible homomorphism
element is an integer modulo 2 and the second element is an integer modulo 3, with component-wise addition and multiplication modulo 2 and 3. These rings
Isomorphism
Set of residue classes modulo n, relatively prime to n
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
Reduced_residue_system
Set with associative invertible operation
In mathematics, a group is a set with an operation that combines any two elements of the set to produce a third element within the same set and the following
Group_(mathematics)
Natural number
it the first cube-sum number greater than one. A number that is 4 or 5 modulo 9 cannot be represented as the sum of three cubes. There are nine Heegner
9
Overview of and topical guide to discrete mathematics
to a number Up to – Mathematical statement of uniqueness, except for an equivalent structure Modular arithmetic – Computation modulo a fixed integer Characterization
Outline of discrete mathematics
Outline_of_discrete_mathematics
Mathematical notion of infinitesimal difference
In mathematics, differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal
Differential_(mathematics)
Type of number sequence
a3, ...) of real numbers is said to be equidistributed modulo 1 or uniformly distributed modulo 1 if the sequence of the fractional parts of an, denoted
Equidistributed_sequence
Performing order of mathematical operations
In mathematics and computer programming, the order of operations is a collection of conventions about which arithmetic operations to perform first in
Order_of_operations
Mathematical investigation of Sudoku
\mathbb {Z} _{n}} the group of pairs, adding each component separately modulo some n {\displaystyle n} . By omitting one of the components, we suddenly
Mathematics_of_Sudoku
Mathematical concept
denoted as X / R , {\displaystyle X/R,} and is called X {\displaystyle X} modulo R {\displaystyle R} (or the quotient set of X {\displaystyle X} by R {\displaystyle
Equivalence_class
Algebraic structure with addition and multiplication
In mathematics, a ring is an algebraic structure consisting of a set with two binary operations typically called addition and multiplication and denoted
Ring_(mathematics)
Number divisible only by 1 and itself
algebra, the ability to perform division means that modular arithmetic modulo a prime number forms a field or, more specifically, a finite field, while
Prime_number
Mathematical sequence
multiples of an irrational α, 0, α, 2α, 3α, 4α, ... is equidistributed modulo 1. In other words, the sequence of the fractional parts of each term will
Weyl_sequence
Generalization of vector spaces from fields to rings
containing torsion elements do not. (For example, in the group of integers modulo 3, one cannot find even one element that satisfies the definition of a linearly
Module_(mathematics)
downstairs, as in "bringing a term upstairs". up to, modulo, mod out by An extension to mathematical discourse of the notions of modular arithmetic. A statement
Glossary of mathematical jargon
Glossary_of_mathematical_jargon
Algebraic structure
prime field of order p {\displaystyle p} may be constructed as the integers modulo p {\displaystyle p} , Z / p Z {\displaystyle \mathbb {Z} /p\mathbb {Z} }
Finite_field
Mathematical statement of uniqueness, except for an equivalent structure
informal contexts, mathematicians often use the word modulo (or simply mod) for similar purposes, as in "modulo isomorphism". Objects that are distinct up to
Up_to
Algebraic structure with addition, multiplication, and division
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on
Field_(mathematics)
Mathematical structure
In mathematics, a building (also Tits building, named after Jacques Tits) is a combinatorial and geometric structure which simultaneously generalizes
Building_(mathematics)
Circulation density in a vector field
fields, and the 3-dimensional fibers to vector fields, as described below. Modulo suitable identifications, the three nontrivial occurrences of the exterior
Curl_(mathematics)
Problem in number theory
mathematics Is there a number that is not 4 or 5 modulo 9 and that cannot be expressed as a sum of three cubes? More unsolved problems in mathematics
Sums_of_three_cubes
Game of strategy
known as "bitwise xor" or "vector addition over GF(2)" (bitwise addition modulo 2). Within combinatorial game theory it is usually called the nim-sum, as
Nim
Algorithm for public-key cryptography
formulation used a shared-secret-key created from exponentiation of some number, modulo a prime number. However, they left open the problem of realizing a one-way
RSA_cryptosystem
Concept in modular arithmetic
remainder after dividing ax by the integer m is 1. If a does have an inverse modulo m, then there is an infinite number of solutions of this congruence, which
Modular multiplicative inverse
Modular_multiplicative_inverse
Branch of mathematical logic
sets of natural numbers, and modulo this representation can be studied in second-order arithmetic. Reverse mathematics makes use of several subsystems
Reverse_mathematics
Numbers obtained by adding the two previous ones
determined by the value of p modulo 5. If p is congruent to 1 or 4 modulo 5, then p divides Fp−1, and if p is congruent to 2 or 3 modulo 5, then, p divides Fp+1
Fibonacci_sequence
Algebraic structure associated with a topological space
quotient group H n = Z n / B n {\displaystyle H_{n}=Z_{n}/B_{n}} of cycles modulo boundaries. One can endow chain complexes with additional structure: for
Homology_(mathematics)
Problem of inverting exponentiation in groups
this concept to a cyclic group. A simple example is the group of integers modulo a prime number (such as 5) under modular multiplication of nonzero elements
Discrete_logarithm
Russian mathematician (1821–1894)
difference between the number of primes that are congruent to 3 (modulo 4) and 1 (modulo 4). Chebyshev was the first person to think systematically in terms
Pafnuty_Chebyshev
Unsolved problem in mathematics
in mathematics In mathematics, specifically in number theory, Newman's conjecture is a conjecture about the behavior of the partition function modulo any
Newman's_conjecture
Natural number
so 57 is a deficient number. Since both prime factors are congruent to 3 modulo 4, 57 = 3 ⋅ 19 {\displaystyle 57=3\cdot 19} is a Blum integer. It is a Leyland
57_(number)
Algorithm for shuffling a finite sequence
cost of eliminating "modulo bias" when generating random integers for a Fisher–Yates shuffle depends on the approach (classic modulo, floating-point multiplication
Fisher–Yates_shuffle
Methods of error detection and correction in communications
operations. A CRC is a checksum in a strict mathematical sense, as it can be expressed as the weighted modulo-2 sum of per-bit syndromes, but that word
Mathematics of cyclic redundancy checks
Mathematics_of_cyclic_redundancy_checks
Group obtained by aggregating similar elements of a larger group
structure is "factored out"). For example, the cyclic group of addition modulo n can be obtained from the group of integers under addition by identifying
Quotient_group
Condition of an optimization problem which the solution must satisfy
Nonlinear programming Restriction Satisfiability modulo theories Takayama, Akira (1985). Mathematical Economics (2nd ed.). New York: Cambridge University
Constraint_(mathematics)
Topics referred to by the same term
quotient ring of numbers modulo 2) The terms 1+1, One Plus One, or One and One may refer to: 1 + 1 + 1 + 1 + ⋯, a mathematical divergent series 1+1 (TV
1+1
Arithmetic operation
modulo 12 has twelve elements; it inherits an addition operation from the integers that is central to musical set theory. The set of integers modulo 2
Addition
Probabilistic primality test
a prime, then the only square roots of 1 modulo n are 1 and −1. Proof Certainly 1 and −1, when squared modulo n, always yield 1. It remains to show that
Miller–Rabin_primality_test
Amount left over after computation
not of theoretical importance in mathematics; however, many programming languages implement this definition (see Modulo operation). Long Division: A traditional
Remainder
American domestic terrorist (1942–2023)
YOO-nə-bom-ər), was an American mathematician and domestic terrorist. A mathematics prodigy, he abandoned his academic career in 1969 to pursue a reclusive
Ted_Kaczynski
Generalization of algebraic variety
In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of an algebraic variety in several ways, such as taking
Scheme_(mathematics)
A prime p divides a^p–a for any integer a
(2013-12-11). "4.5.1. Lemma (Roots of unity modulo a prime)". Primality Testing for Beginners. American Mathematical Soc. ISBN 9780821898833. Albert, A. Adrian
Fermat's_little_theorem
Visualization of the prime numbers formed by arranging the integers into a spiral
mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in Scientific American a short time later. It is constructed
Ulam_spiral
Integral expressing the amount of overlap of one function as it is shifted over another
In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions f {\displaystyle f} and g {\displaystyle
Convolution
Number system extending the rational numbers
arithmetic modulo a positive integer n consists of "approximating" every integer by the remainder of its division by n, called its residue modulo n. The main
P-adic_number
Algorithm for fast modular multiplication
RSA and Diffie–Hellman key exchange are based on arithmetic operations modulo a large odd number, and for these cryptosystems, computations using Montgomery
Montgomery modular multiplication
Montgomery_modular_multiplication
Number that, when added to the original number, yields the additive identity
that a + x ≡ 0 (mod n) and always exists. For example, the inverse of 3 modulo 11 is 8, as 3 + 8 ≡ 0 (mod 11). In a Boolean ring, which has elements {
Additive_inverse
In mathematics, invariant of square matrices
In mathematics, the determinant is a scalar-valued function of the entries of a square matrix. The determinant of a matrix A is commonly denoted det(A)
Determinant
Mathematical concept
general, may not be reduced modulo 2). It is then possible to reduce all coefficients modulo 2, which will give a modular form modulo 2. Modular forms are generated
Modular_forms_modulo_p
Type of mathematical expression
In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the
Polynomial
This is a timeline of women in mathematics. Before 350: Pandrosion, a Greek mathematician known for an approximate solution to doubling the cube and a
Timeline of women in mathematics
Timeline_of_women_in_mathematics
Number of ways to pair up n objects
In mathematics, the telephone numbers or the involution numbers form a sequence of integers that count the ways n people can be connected by person-to-person
Telephone number (mathematics)
Telephone_number_(mathematics)
Theorem on modular exponentiation
n ) {\displaystyle a^{\varphi (n)}} is congruent to 1 {\displaystyle 1} modulo n, where φ {\displaystyle \varphi } denotes Euler's totient function; that
Euler's_theorem
Computer arithmetic error
arithmetic with unsigned integers to be arithmetic modulo 2W, where W is the word size, which is mathematically well-defined and only has representable values
Integer_overflow
number theory, a kth root of unity modulo n for positive integers k, n ≥ 2, is a root of unity in the ring of integers modulo n; that is, a solution x to the
Root_of_unity_modulo_n
Straight figure with zero width and depth
parameters, φ and p, to be specified. If p > 0, then φ is uniquely defined modulo 2π. On the other hand, if the line is through the origin (c = p = 0), one
Line_(geometry)
Function in mathematical number theory
algebraic terms, λ(n) is the exponent of the multiplicative group of integers modulo n. As this is a finite abelian group, there must exist an element whose
Carmichael_function
Special subset of a partially ordered set
In mathematics, a filter or order filter is a special subset of a partially ordered set (poset), describing "large" or "eventual" elements. Filters appear
Filter_(mathematics)
Open problem on 3x+1 and x/2 functions
Unsolved problem in mathematics For even numbers, divide by 2; For odd numbers, multiply by 3 and add 1. With enough repetition, do all positive integers
Collatz_conjecture
Three linked but pairwise separated rings
In mathematics, the Borromean rings are three simple closed curves in three-dimensional space that are topologically linked and cannot be separated from
Borromean_rings
Result in modular arithmetic
modulo a prime number p, then this root can be lifted to a unique root modulo any higher power of p. More generally, if a polynomial factors modulo p
Hensel's_lemma
About simultaneous modular congruences
/n_{k}\mathbb {Z} } between the ring of integers modulo N and the direct product of the rings of integers modulo the ni. This means that for doing a sequence
Chinese_remainder_theorem
Some remarkable congruences for the partition function
Ono, Ken (2000). "Distribution of the partition function modulo m". Annals of Mathematics. Second Series. 151 (1): 293–307. arXiv:math/0008140. Bibcode:2000math
Ramanujan's_congruences
Mapping arbitrary data to fixed-size values
+ r0 is any nonzero polynomial modulo 2 with at most t nonzero coefficients, then R(x) is not a multiple of P(x) modulo 2. If follows that the corresponding
Hash_function
Unproved conjecture in mathematics
Vladimir (2010). "On the Birch–Swinnerton-Dyer quotients modulo squares". Annals of Mathematics. 172 (1): 567–596. arXiv:math/0610290. doi:10.4007/annals
Birch and Swinnerton-Dyer conjecture
Birch_and_Swinnerton-Dyer_conjecture
Mathematical table
In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for
Multiplication_table
Unique numeric book identifier since 1970
(11 minus the remainder of the sum of the products modulo 11) modulo 11. Taking the remainder modulo 11 a second time accounts for the possibility that
ISBN
Mathematical connection between field theory and group theory
Neither does it have linear factors modulo 2 or 3. The Galois group of f(x) modulo 2 is cyclic of order 6, because f(x) modulo 2 factors into polynomials of
Galois_theory
Doughnut-shaped surface of revolution
Rn under integral shifts in any coordinate. That is, the n-torus is Rn modulo the action of the integer lattice Zn (with the action being taken as vector
Torus
Standard representation of a mathematical object
In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical
Canonical_form
Mathematical group that can be generated as the set of powers of a single element
group of order n is isomorphic to the additive group of Z/nZ, the integers modulo n. Every cyclic group is an abelian group (meaning that its group operation
Cyclic_group
(modulo the roots of unity) for the unit group of the ring of integers of a number field, when that group has rank 1 (i.e. when the unit group modulo its
Fundamental unit (number theory)
Fundamental_unit_(number_theory)
Cantor algebra is the complete Boolean algebra of Borel subsets of the reals modulo meager sets (Balcar & Jech 2006). It is isomorphic to the completion of
Cantor_algebra
In mathematical logic, a well-formed formula with no free variables
that render all sentences as being true is known as the satisfiability modulo theories problem. For the interpretation of formulas, a domain of discourse
Sentence_(mathematical_logic)
Prime pair of the form (p, 2p+1)
and Paul Zimmermann announced the computation of a discrete logarithm modulo the 240-digit (795 bit) prime RSA-240 + 49204 (the first safe prime above
Safe and Sophie Germain primes
Safe_and_Sophie_Germain_primes
Topics referred to by the same term
cyclically ordered sequences of symbols modulo certain symmetries Cyclic (mathematics), a list of mathematics articles with "cyclic" in the title Cyclic
Cycle
Mathematical idealization of the surface of a body
In mathematics, a surface is a mathematical model of the common concept of a surface. It is a generalization of a plane, but, unlike a plane, it may be
Surface_(mathematics)
Irreducible polynomial whose roots are nth roots of unity
In mathematics, the n {\displaystyle n} -th cyclotomic polynomial, for any positive integer n {\displaystyle n} , is the unique irreducible polynomial
Cyclotomic_polynomial
5th century BC Greek mathematician
congruent to 1 modulo 8 (since x {\displaystyle x} and y {\displaystyle y} can be assumed odd, so their squares are congruent to 1 modulo 8. In one axiomatic
Theodorus_of_Cyrene
Gives conditions for the solvability of quadratic equations modulo prime numbers
arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. Due to its subtlety, it has many formulations, but the most
Quadratic_reciprocity
Motion of a certain space that preserves at least one point
origin; see below for details. Composition of rotations sums their angles modulo 1 turn, which implies that all two-dimensional rotations about the same
Rotation_(mathematics)
MODULO MATHEMATICS
MODULO MATHEMATICS
Boy/Male
Gujarati, Hindu, Indian, Kannada, Marathi
Enjoyment
Girl/Female
Christian & English(British/American/Australian)
Model or Pattern
Boy/Male
Egyptian
To model.
Girl/Female
Hindu, Indian, Marathi
Sacred Thread; Mother
Male
Spanish
Spanish form of Latin Theodulus, TEÓDULO means "god-slave."
Boy/Male
Muslim
Sample, Model, Paragon
Surname or Lastname
English
English : from the Middle English female personal name Mau(l)d, a reduced form of the Norman name Mathilde, Matilda, composed of the Germanic elements maht ‘might’, ‘strength’ + hild ‘strife’, ‘battle’. The learned form Matilda was much less common in the Middle Ages than the vernacular forms Mahalt, Maud and the reduced pet form Till. The name was borne by the daughter of Henry I of England, who disputed the throne of England with her cousin Stephen for a number of years (1137–48). In Germany the popularity of the name in the Middle Ages was augmented by its being borne by a 10th-century saint, wife of Henry the Fowler and mother of Otto the Great.
Girl/Female
Hindu, Indian, Traditional
Model; Idea
Female
English
Variant spelling of Middle English Mauld, MOULD means "mighty in battle."
Boy/Male
Arabic, Assamese, Indian, Muslim
Main; New
Boy/Male
Arabic, Muslim
Model; Example
Boy/Male
Hindu
Name of Lord Shiva
Girl/Female
African, Australian, Nigerian
I am Grateful; Gratefulness
Boy/Male
Muslim
Model, Example
Boy/Male
Hindu, Indian, Telugu
Lord Shiva; Wearing
Boy/Male
Arabic, Muslim
Sample; Model; Paragon
Girl/Female
Arabic, Muslim
Example; Model; Demo
Surname or Lastname
English
English : variant of Mule.
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Tamil, Telugu
Attractive
Boy/Male
French, German, Teutonic
Rich
MODULO MATHEMATICS
MODULO MATHEMATICS
Girl/Female
Indian, Telugu
Ecstasy
Girl/Female
Tamil
Loveleen | லோவேலீந
Love to God
Girl/Female
American, Australian, British, Chinese, Christian, English, Irish
Sorrow; Grief; Fear or Raging Woman; Young Girl
Boy/Male
Greek, Indian
Winner of Battle
Male
English
Modern English name derived from the Greek word neos, NEO means "new." Compare with another form of Neo.
Girl/Female
Tamil
Beautiful
Male
English
English surname transferred to forename use, from the Norman French word march, MARCH means "boundary." Compare with other forms of March.
Surname or Lastname
English
English : topographic name from Middle English feldes, plural or possessive of feld ‘open country’. This name is also found as a translation of equivalent names in other languages, in particular French Deschamps, Duchamp.
Boy/Male
Hindu, Indian
King; Lovable
Girl/Female
Hindu, Indian
Truth and Knowledge
MODULO MATHEMATICS
MODULO MATHEMATICS
MODULO MATHEMATICS
MODULO MATHEMATICS
MODULO MATHEMATICS
imp. & p. p.
of Moult
a.
Of or pertaining to mode, modulation, module, or modius; as, modular arrangement; modular accent; modular measure.
n.
The size of some one part, as the diameter of semi-diameter of the base of a shaft, taken as a unit of measure by which the proportions of the other parts of the composition are regulated. Generally, for columns, the semi-diameter is taken, and divided into a certain number of parts, called minutes (see Minute), though often the diameter is taken, and any dimension is said to be so many modules and minutes in height, breadth, or projection.
p. pr. & vb. n.
of Mould
n.
Something intended to serve, or that may serve, as a pattern of something to be made; a material representation or embodiment of an ideal; sometimes, a drawing; a plan; as, the clay model of a sculpture; the inventor's model of a machine.
a.
Suitable to be taken as a model or pattern; as, a model house; a model husband.
v. t.
To form into a particular shape; to shape; to model; to fashion.
n.
To model; also, to modulate.
n.
A fixed part of a module. See Module.
pl.
of Morula
pl.
of Modulus
n.
Anything which serves, or may serve, as an example for imitation; as, a government formed on the model of the American constitution; a model of eloquence, virtue, or behavior.
n.
A fixed compensation or equivalent given instead of payment of tithes in kind, expressed in full by the phrase modus decimandi.
v. i.
To make a copy or a pattern; to design or imitate forms; as, to model in wax.
p. pr. & vb. n.
of Moult
v. t.
To plan or form after a pattern; to form in model; to form a model or pattern for; to shape; to mold; to fashion; as, to model a house or a government; to model an edifice according to the plan delineated.
n.
A model or measure.