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Luhn algorithm. The Luhn algorithm or Luhn formula, also known as the " modulus 10" or "mod 10" algorithm, named after its creator, IBM scientist Hans Peter Luhn, is a simple check digit formula used to validate a variety of identification numbers. It is described in US patent 2950048A, granted on 23 August 1960. [ 1]
Modular exponentiation is the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus); that is, c = be mod m. From the definition of division, it follows that 0 ≤ c < m . For example, given b = 5, e = 3 and m = 13, dividing 53 = 125 by 13 leaves a remainder of c = 8 .
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. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...
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 to 1 with respect to the modulus m. [ 1] In the standard notation of modular arithmetic this congruence is written as.
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. [1]
A modulus is a formal product [3] [4] where p runs over all places of K, finite or infinite, the exponents ν ( p) are zero except for finitely many p. If K is a number field, ν ( p ) = 0 or 1 for real places and ν ( p ) = 0 for complex places. If K is a function field, ν ( p ) = 0 for all infinite places. In the function field case, a ...
The United States Court of Appeals for the Fifth Circuit (in case citations, 5th Cir.) is one of the 13 United States courts of appeals. It has appellate jurisdiction over the U.S. district courts in the following federal judicial districts : The Fifth Circuit has 17 active judgeships, and is headquartered at the John Minor Wisdom United States ...
Barrett reduction. In modular arithmetic, Barrett reduction is a reduction algorithm introduced in 1986 by P.D. Barrett. [ 1] A naive way of computing. would be to use a fast division algorithm. Barrett reduction is an algorithm designed to optimize this operation assuming is constant, and , replacing divisions by multiplications.