In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus...
29 KB (3,602 words) - 18:28, 25 August 2024
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...
24 KB (3,639 words) - 06:47, 26 January 2024
x} for intervals near a number x {\displaystyle x} ). Modular arithmetic modifies usual arithmetic by only using the numbers { 0 , 1 , 2 , … , n − 1 } {\displaystyle...
116 KB (14,108 words) - 23:59, 15 August 2024
Universal hashing (section Avoiding modular arithmetic)
multiply-shift scheme described by Dietzfelbinger et al. in 1997. By avoiding modular arithmetic, this method is much easier to implement and also runs significantly...
29 KB (4,875 words) - 10:36, 18 April 2024
Residue number system (redirect from Multi-modular arithmetic)
set of modular values. Using a residue numeral system for arithmetic operations is also called multi-modular arithmetic. Multi-modular arithmetic is widely...
13 KB (1,596 words) - 08:28, 9 July 2024
implement integer arithmetic operations using saturation arithmetic; instead, they use the easier-to-implement modular arithmetic, in which values exceeding...
8 KB (1,075 words) - 02:19, 13 August 2024
Modulo (redirect from Modular operation)
F. Gauss's introduction of modular arithmetic in 1801. Modulo (mathematics), general use of the term in mathematics Modular exponentiation Turn (angle)...
46 KB (3,351 words) - 10:59, 15 August 2024
means 10 ≡ 1 ( mod 3 ) {\displaystyle 10\equiv 1{\pmod {3}}} (see modular arithmetic). The same for all the higher powers of 10: 10 n ≡ 1 n ≡ 1 ( mod 3...
54 KB (6,861 words) - 19:25, 23 July 2024
signals to perform calculations. There are many other types of arithmetic. Modular arithmetic operates on a finite set of numbers. If an operation would result...
165 KB (16,366 words) - 19:38, 22 August 2024
In modular arithmetic computation, Montgomery modular multiplication, more commonly referred to as Montgomery multiplication, is a method for performing...
28 KB (3,847 words) - 07:52, 4 May 2024
Arithmetic dynamics Arithmetic of abelian varieties Birch and Swinnerton-Dyer conjecture Moduli of algebraic curves Siegel modular variety Siegel's theorem...
15 KB (1,464 words) - 19:56, 6 May 2024
factors Formula for primes Factorization RSA number Fundamental theorem of arithmetic Square-free Square-free integer Square-free polynomial Square number Power...
10 KB (935 words) - 23:13, 8 August 2024
1)\\&=0+27+0+42+24+0+24+3+10+2\\&=132=12\times 11.\end{aligned}}} Formally, using modular arithmetic, this is rendered ( 10 x 1 + 9 x 2 + 8 x 3 + 7 x 4 + 6 x 5 + 5 x 6...
61 KB (6,637 words) - 08:44, 6 July 2024
perform modular exponentiation The GNU Multiple Precision Arithmetic Library (GMP) library contains a mpz_powm() function [5] to perform modular exponentiation...
21 KB (2,802 words) - 00:03, 24 March 2024
Unit fraction (category Elementary arithmetic)
produces another unit fraction, but other arithmetic operations do not preserve unit fractions. In modular arithmetic, unit fractions can be converted into...
24 KB (2,978 words) - 15:11, 18 August 2024
Group (mathematics) (section Modular arithmetic)
operations of modular arithmetic modify normal arithmetic by replacing the result of any operation by its equivalent representative. Modular addition, defined...
101 KB (13,126 words) - 14:06, 5 August 2024
Pai gow (section Modular arithmetic)
the total number of pips on both tiles in a hand are added using modular arithmetic (modulo 10), equivalent to how a hand in baccarat is scored. The name...
21 KB (1,960 words) - 12:50, 27 April 2024
Morra (game) (section Modular arithmetic)
The game can be expanded for a larger number of players by using modular arithmetic. For n players, each player is assigned a number from zero to n−1...
15 KB (2,177 words) - 04:24, 23 July 2024
theorem of arithmetic. Article 16 of Gauss's Disquisitiones Arithmeticae is an early modern statement and proof employing modular arithmetic. Every positive...
22 KB (3,201 words) - 18:14, 23 August 2024
Quotient group (section Integer modular arithmetic)
\mathbb {Z} } ) Free group Modular groups PSL(2, Z {\displaystyle \mathbb {Z} } ) SL(2, Z {\displaystyle \mathbb {Z} } ) Arithmetic group Lattice Hyperbolic...
21 KB (3,766 words) - 00:20, 17 July 2024
Euler's totient function (category Modular arithmetic)
1 numbers are all relatively prime to pk. The fundamental theorem of arithmetic states that if n > 1 there is a unique expression n = p 1 k 1 p 2 k 2...
44 KB (6,473 words) - 18:17, 31 July 2024
from modular arithmetic: By the above lemma, r = p v m n , {\textstyle r=p^{v}{\frac {m}{n}},} where m and n are integers coprime with p. The modular inverse...
43 KB (7,563 words) - 20:47, 16 August 2024
Barrett reduction (category Modular arithmetic)
In modular arithmetic, Barrett reduction is a reduction algorithm introduced in 1986 by P.D. Barrett. A naive way of computing c = a mod n {\displaystyle...
11 KB (1,848 words) - 22:59, 13 August 2023
Casting modulus used in Chvorinov's rule. Modulus (modular arithmetic), base of modular arithmetic Modulus, the absolute value of a real or complex number...
2 KB (252 words) - 05:55, 12 January 2024
Quadratic residue (redirect from Modular square root)
abstract mathematical concept from the branch of number theory known as modular arithmetic, quadratic residues are now used in applications ranging from acoustical...
54 KB (5,557 words) - 19:40, 15 May 2024
group" comes from the relation to moduli spaces and not from modular arithmetic. The modular group Γ is the group of linear fractional transformations of...
25 KB (3,317 words) - 11:59, 8 November 2023
Primitive root modulo n (category Modular arithmetic)
In modular arithmetic, 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. That is, g is a primitive...
22 KB (2,502 words) - 00:51, 6 May 2024
Mean (section Arithmetic mean (AM))
points. Angles, times of day, and other cyclical quantities require modular arithmetic to add and otherwise combine numbers. In all these situations, there...
16 KB (2,127 words) - 08:00, 23 August 2024
Multiplicative inverse (redirect from Arithmetic inverse)
integer reciprocal, and so the integers are not a field. In modular arithmetic, the modular multiplicative inverse of a is also defined: it is the number...
15 KB (2,359 words) - 21:49, 29 June 2024
Addition (redirect from + (arithmetic))
signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition...
74 KB (9,560 words) - 22:53, 20 August 2024