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Number in {..., –2, –1, 0, 1, 2, ...}
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations
Integer
Decomposition of an integer as a sum of positive integers
partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only
Integer_partition
Mathematical optimization problem restricted to integers
An integer programming, also known as integer optimization, problem is a mathematical optimization or feasibility program in which some or all of the variables
Integer_programming
Decomposition of a number into a product
decomposition of a positive integer into a product of integers. Every positive integer greater than 1 is either the product of two or more integer factors greater
Integer_factorization
Computer arithmetic error
In computer programming, an integer overflow occurs when an arithmetic operation on integers attempts to create a numeric value that is outside of the
Integer_overflow
Any number that is not an integer but is very close to one
mathematics, an almost integer (or near-integer) is any number that is not an integer but is very close to one. Almost integers may be considered interesting
Almost_integer
Online database of integer sequences
The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences. It was created and maintained by Neil Sloane while researching
On-Line Encyclopedia of Integer Sequences
On-Line_Encyclopedia_of_Integer_Sequences
Complex number whose real and imaginary parts are both integers
number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and
Gaussian_integer
Asian tree related to breadfruit and jackfruit
Artocarpus integer, commonly known as chempedak or cempedak, is a species of tree in the family Moraceae, in the same genus as breadfruit and jackfruit
Artocarpus_integer
Number used for counting
2, 3, and so on, possibly excluding 0. The terms positive integers, non-negative integers, whole numbers, and counting numbers are also used. The set
Natural_number
Datum of integral data type
computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers. Integral data types may
Integer_(computer_science)
Complex number that solves a monic polynomial with integer coefficients
number theory, an algebraic integer is a complex number that is integral over the integers. That is, an algebraic integer is a complex root of some monic
Algebraic_integer
isl (integer set library) is a portable C library for manipulating sets and relations of integer points bounded by linear constraints. The following operations
Integer_set_library
Topics referred to by the same term
Integer function may refer to: Integer-valued function, an integer function Floor function, sometimes referred as the integer function, INT Arithmetic
Integer_function
Two numbers without shared prime factors
In number theory, two integers a and b are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them
Coprime_integers
Complex number whose mapping on a coordinate plane produces a triangular lattice
In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the
Eisenstein_integer
Computation modulo a fixed integer
mathematics, modular arithmetic is a system of arithmetic operations for integers, differing from the usual ones in that numbers "wrap around" when reaching
Modular_arithmetic
Ordered list of whole numbers
In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers. An integer sequence may be specified explicitly by giving a formula
Integer_sequence
Method to solve optimization problems
unknown variables are required to be integers, then the problem is called an integer programming (IP) or integer linear programming (ILP) problem. In
Linear_programming
Nearest integers from a number
returns the greatest integer less than or equal to x, written ⌊x⌋ or floor(x). Similarly, the ceiling function returns the least integer greater than or equal
Floor_and_ceiling_functions
Number system extending the rational numbers
integer (possibly negative), and each a i {\displaystyle a_{i}} is an integer such that 0 ≤ a i < p . {\displaystyle 0\leq a_{i}<p.} A p-adic integer
P-adic_number
Product of two distinct primes ≡ 3 (mod 4)
form 4t + 3, for some integer t. Integers of this form are referred to as Blum primes. This means that the factors of a Blum integer are Gaussian primes
Blum_integer
Lattice group in Euclidean space whose points are integer n-tuples
n-tuples of integers. The two-dimensional integer lattice is also called the square lattice (or grid lattice) and the three-dimensional integer lattice is
Integer_lattice
Integer that divides another integer
mathematics, a divisor of an integer n , {\displaystyle n,} also called a factor of n , {\displaystyle n,} is an integer m {\displaystyle m} that may
Divisor
Mathematical procedure
An integer relation between a set of real numbers x1, x2, ..., xn is a set of integers a1, a2, ..., an, not all 0, such that a 1 x 1 + a 2 x 2 + ⋯ + a
Integer_relation_algorithm
Replacing a number with a simpler value
reporting many computations – especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as
Rounding
This is a list of notable integer sequences with links to their entries in the On-Line Encyclopedia of Integer Sequences. OEIS core sequences Index to
List_of_integer_sequences
Triangle with integer side lengths
An integer triangle or integral triangle is a triangle all of whose side lengths are integers. A rational triangle is one whose side lengths are rational
Integer_triangle
Rational number equal to an integer plus 1/2
mathematics, a half-integer is a number of the form n + 1 2 , {\displaystyle n+{\tfrac {1}{2}},} where n {\displaystyle n} is an integer. For example, 4 1
Half-integer
Data types supported by the C programming language
data elements. The C language provides basic arithmetic types, such as integer and real number types, and syntax to build array and compound types. The
C_data_types
Number in base-10 numeral system
radix (base). Decimal systems are the global standard for denoting integer and non-integer numbers. The way of denoting numbers in a decimal system is often
Decimal
the Germanic concept of 1200 as a long thousand. It is the first 4-digit integer. The decimal representation for one thousand is 1000—a one followed by
1000_(number)
Class of subatomic particle
(/ˈboʊzɒn/ /ˈboʊsɒn/) is a subatomic particle whose spin quantum number has an integer value (0, 1, 2, ...). The class of bosons is one of the two fundamental
Boson
Algebraic construction
ring of all algebraic integers contained in K {\displaystyle K} . An algebraic integer is a root of a monic polynomial with integer coefficients: x n +
Ring_of_integers
Natural number
numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. "13.1.2 Integer Types (Exact Value) - INTEGER, INT, SMALLINT, TINYINT, MEDIUMINT
1,000,000,000
Length of expression as combination of 1s
In number theory, the complexity of an integer is the smallest number of ones that can be used to represent it using ones and any number of additions
Integer_complexity
Number-theoretic concept
In mathematics, a profinite integer is an element of the ring (sometimes pronounced as zee-hat or zed-hat) Z ^ = lim ← Z / n Z , {\displaystyle {\widehat
Profinite_integer
BASIC interpreter of the Apple I and original Apple II computers
Integer BASIC is a BASIC interpreter written by Steve Wozniak for the Apple I and Apple II computers. Originally available on cassette for the Apple I
Integer_BASIC
Root of a quadratic polynomial with a unit leading coefficient
theory, quadratic integers are a generalization of the usual integers to quadratic fields. A complex number is called a quadratic integer if it is a root
Quadratic_integer
Arithmetic operation
with remainder or Euclidean division of two natural numbers provides an integer quotient, which is the number of times the second number is completely
Division_(mathematics)
Matrix whose entries are integers
In mathematics, an integer matrix is a matrix whose entries are all integers. Examples include binary matrices, the zero matrix, the matrix of ones, the
Integer_matrix
Type of subatomic particle
subatomic particle that follows Fermi–Dirac statistics. Fermions have a half-integer spin (spin 1/2, spin 3/2, etc.) and obey the Pauli exclusion principle
Fermion
Kleinian integer is a complex number of the form m + n 1 + − 7 2 {\displaystyle m+n{\frac {1+{\sqrt {-7}}}{2}}} , with m and n rational integers. They are
Kleinian_integer
Computational task of sorting whole numbers
science, integer sorting is the algorithmic problem of sorting a collection of data values by integer keys. Algorithms designed for integer sorting may
Integer_sorting
computational complexity theory, an integer circuit is a circuit model of computation in which inputs to the circuit are sets of integers and each gate of the circuit
Integer_circuit
Type of mathematical expression
addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms. An example of a polynomial of
Polynomial
Greatest integer less than or equal to square root
number theory, the integer square root (isqrt) of a non-negative integer n is the non-negative integer m which is the greatest integer less than or equal
Integer_square_root
Extension of the factorial function
{\displaystyle z} except non-positive integers, and Γ ( n ) = ( n − 1 ) ! {\displaystyle \Gamma (n)=(n-1)!} for every positive integer n {\displaystyle n} . The
Gamma_function
Natural number
of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences
1,000,000,000,000
Integer side lengths of a right triangle
A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), a well-known
Pythagorean_triple
Property of being an even or odd number
In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not. For
Parity_(mathematics)
Species of beetle
Prionus integer is a species of long-horned beetle in the family Cerambycidae. It is endemic to the United States. "Prionus integer". Integrated Taxonomic
Prionus_integer
Number that permute or shift cyclically when multiplied by another number
mathematics, the transposable integers are integers that permute or shift cyclically when they are multiplied by another integer n {\displaystyle n} . Examples
Transposable_integer
Used to count, measure, and label
Hindu–Arabic numeral system, a decimal system which can display any non-negative integer using a combination of ten Arabic numeral symbols called digits. Numerals
Number
Natural number
number preceding a cube. As an early prime number in the series of positive integers, the number seven has symbolic associations in religion, mythology, superstition
7
Number without repeated prime factors
In mathematics, a square-free integer (or squarefree integer) is an integer that is divisible by no square number other than 1. That is, its prime factorization
Square-free_integer
Family of solutions to related differential equations
are when α {\displaystyle \alpha } is an integer or a half-integer. When α {\displaystyle \alpha } is an integer, the resulting Bessel functions are often
Bessel_function
Arithmetic operation
numbers: the base, b, and the exponent or power, n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that
Exponentiation
mathematics, an integer-valued function is a function whose values are integers. In other words, it is a function that assigns an integer to each member
Integer-valued_function
House in United Kingdom, United Kingdom
The INTEGER Millennium House is a demonstration house in Watford, England that opened to the public in 1998. It was renamed The Smart Home after being
INTEGER_Millennium_House
Product of the prime factors of an integer
In number theory, the radical of a positive integer n is defined as the product of the distinct prime numbers dividing n. Each prime factor of n occurs
Radical_of_an_integer
The study of integer points in convex polyhedra is motivated by questions such as "how many nonnegative integer-valued solutions does a system of linear
Integer points in convex polyhedra
Integer_points_in_convex_polyhedra
Integers have unique prime factorizations
factorization theorem and prime factorization theorem, states that every integer greater than 1 is either prime or can be represented uniquely as a product
Fundamental theorem of arithmetic
Fundamental_theorem_of_arithmetic
Polynomial equation whose integer solutions are sought
a Diophantine equation is a polynomial equation with integer coefficients, for which only integer solutions are of interest. A linear Diophantine equation
Diophantine_equation
Species of sawfly
Janus integer, the currant stem girdler, is a species of stem sawfly in the family Cephidae native to North America. "Janus integer Report". Integrated
Janus_integer
Natural number
N. J. A. Sloane. "A005278: Noncototients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01. Wikimedia Commons has
10
Natural number
1867. In computing, this number is the largest value that a signed 32-bit integer field can hold. At the time of its discovery, 2,147,483,647 was the largest
2,147,483,647
Index of articles associated with the same name
In mathematics, a nonstandard integer may refer to Hyperinteger, the integer part of a hyperreal number an integer in a non-standard model of arithmetic
Nonstandard_integer
branch of mathematics, the integer broom topology is an example of a topology on the so-called integer broom space X. The integer broom space X is a subset
Integer_broom_topology
Polynomial with integer value for integer input
( n ) {\displaystyle P(n)} is an integer for every integer n. Every polynomial with integer coefficients is integer-valued, but the converse is not true
Integer-valued_polynomial
17th-century conjecture proved by Andrew Wiles in 1994
conjecture, especially in older texts) states that there are no positive integers a , b , c , n {\displaystyle a,b,c,n} with n > 2 {\displaystyle n>2} such
Fermat's_Last_Theorem
Notation for representing an integer in source code
In computer science, an integer literal is a kind of literal for an integer whose value is directly represented in source code. For example, in the assignment
Integer_literal
Encoding method for variable-length integers
bytes) to represent an arbitrarily large integer. A VLQ is essentially a base-128 representation of an unsigned integer with the addition of the eighth bit
Variable-length_quantity
Statistical distribution
generalized integer gamma distribution (GIG) is the distribution of the sum of independent gamma distributed random variables, all with integer shape parameters
Generalized integer gamma distribution
Generalized_integer_gamma_distribution
Academic journal
Journal of Integer Sequences is a peer-reviewed open-access academic journal in mathematics, specializing in research papers about integer sequences.
Journal_of_Integer_Sequences
Root-finding algorithm
treating the bits representing the floating-point number as a 32-bit integer, a logical shift right by one bit is performed and the result subtracted
Fast_inverse_square_root
Efficient variable-length integer encoding
arbitrarily large integers in a small number of bytes. LEB128 is used in the DWARF debug file format and the WebAssembly binary encoding for all integer literals
LEB128
Natural number
Encyclopedia of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A259180 (Amicable pairs.)". The On-Line Encyclopedia of Integer Sequences
500_(number)
Electromagnetic effect in physics
The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems
Quantum_Hall_effect
American publishing house
Green Integer is an American publishing house of pocket-sized belles-lettres books, based in Los Angeles, California. It was founded in 1997 by Douglas
Green_Integer
Species of crustacean
Neomysis integer is a species of opossum shrimp found in shallow marine bays and estuaries of Europe, with a transparent greenish or brownish body and
Neomysis_integer
divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, for which n/m is again an integer (which is necessarily also a divisor of n).
Table_of_divisors
A prime p divides a^p–a for any integer a
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 the notation of modular arithmetic,
Fermat's_little_theorem
Finite or infinite ordered list of elements
in these examples, or infinite, such as the sequence of positive even integers (2, 4, 6, 8, ...). The length of a finite sequence is defined as the number
Sequence
Natural number
following 76 and preceding 78. Seventy-seven is the smallest positive integer requiring five syllables in English. 77 is: the 22nd discrete semiprime
77_(number)
Accomplishments in factoring large integers
Integer factorization is the process of determining which prime numbers divide a given positive integer. Doing this quickly has applications in cryptography
Integer_factorization_records
Open problem on 3x+1 and x/2 functions
numbers, multiply by 3 and add 1. With enough repetition, do all positive integers converge to 1? More unsolved problems in mathematics The Collatz conjecture
Collatz_conjecture
Calculations where numbers' precision is only limited by computer memory
for bignums, and others have libraries available for arbitrary-precision integer and floating-point math. Rather than storing values as a fixed number of
Arbitrary-precision arithmetic
Arbitrary-precision_arithmetic
Natural number
number. 604 = 22 × 151. It is a nontotient and the totient sum for first 44 integers. 605 = 5 × 112. It is a Harshad number and the sum of the nontriangular
600_(number)
Amount left over after computation
arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division). In algebra of polynomials
Remainder
Generalization of algebraic integers
Hurwitz integer) is a quaternion whose components are either all integers or all half-integers (halves of odd integers; a mixture of integers and half-integers
Hurwitz_quaternion
Product of numbers from 1 to n
factorial of a non-negative integer n {\displaystyle n} , denoted by n ! {\displaystyle n!} , is the product of all positive integers less than or equal to
Factorial
Natural number
290 theorems describes integer-quadratic matrices that describe all positive integers, by the set of the first fifteen integers, or equivalently, the first
29_(number)
Branch of pure mathematics
rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions
Number_theory
Even integers as sums of two primes
Euler (letter XLIII), in which he proposed the following conjecture: Every integer that can be written as the sum of two primes can also be written as the
Goldbach's_conjecture
Algorithm for fast modular multiplication
} where a ranges across the integers. Each residue class is a set of integers such that the difference of any two integers in the set is divisible by N
Montgomery modular multiplication
Montgomery_modular_multiplication
Natural number
to end in 2. 324 = 22 × 34 = 182. It is the totient sum of the first 32 integers, a square number, and an untouchable number. It is the sum of four consecutive
300_(number)
Binary representation for signed numbers
most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values. As with the
Two's_complement
Combinational digital circuit
combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers. This is in contrast to a floating-point unit (FPU), which
Arithmetic_logic_unit
Natural number
Encyclopedia of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A097942 (Highly totient numbers)". The On-Line Encyclopedia of Integer Sequences
100,000
INTEGER
INTEGER
INTEGER
INTEGER
Girl/Female
American, Australian, British, Danish, English, French
Combination of Rose and Anna; Favour
Female
English
English form of French Nicole, NICHOLE means "victor of the people."Â
Boy/Male
Tamil
Pushpesh | பà¯à®·à¯à®ªà¯‡à®·
Lord of flowers
Girl/Female
Hindu, Indian, Marathi
God Winner
Boy/Male
English
royal.
Girl/Female
Hindu
Boy/Male
Indian
Pearl, Ruby, Name of a precious stone
Boy/Male
Indian
Lord of Truth
Girl/Female
Tamil
One who is courageous
Girl/Female
Gujarati, Hindu, Indian
Happy
INTEGER
INTEGER
INTEGER
INTEGER
INTEGER
n.
That number placed below the line in vulgar fractions which shows into how many parts the integer or unit is divided.
a.
Essential to completeness; constituent, as a part; pertaining to, or serving to form, an integer; integrant.
n.
A complete entity; a whole number, in contradistinction to a fraction or a mixed number.