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Time-keeping on this clock uses arithmetic modulo 12. Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus.
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.
Modulo is a mathematical jargon that was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. [3] Given the integers a, b and n, the expression "a ≡ b (mod n)", pronounced "a is congruent to b modulo n", means that a − b is an integer multiple of n, or equivalently, a and b both share the same remainder when divided by n.
where the modulus m is a prime number or a power of a prime number, the multiplier a is an element of high multiplicative order modulo m (e.g., a primitive root modulo n), and the seed X 0 is coprime to m. Other names are multiplicative linear congruential generator (MLCG) [2] and multiplicative congruential generator (MCG).
A modular multiplicative inverse of an integer a with respect to the modulus m is a solution of the linear congruence a x ≡ 1 ( mod m ) . {\displaystyle ax\equiv 1{\pmod {m}}.} The previous result says that a solution exists if and only if gcd( a , m ) = 1 , that is, a and m must be relatively prime (i.e. coprime).
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Bulk modulus, a measure of compression resistance; Elastic modulus, a measure of stiffness; Shear modulus, a measure of elastic stiffness; Young's modulus, a specific elastic modulus; Modulo operation (a % b, mod(a, b), etc.), in both math and programming languages; results in remainder of a division; Casting modulus used in Chvorinov's rule.