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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]
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 ...
Template:Modulo/doc. Template. : Modulo/doc. This is a documentation subpage for Template:Modulo. It may contain usage information, categories and other content that is not part of the original template page. This template is used on many pages and changes may be widely noticed. Test changes in the template's /sandbox or /testcases subpages, or ...
The dodecagonal number for n is given by the formula ... first n natural numbers congruent to 1 mod 10. ... is the sum of all odd numbers from 4n+1 to 6n+1. See also ...
The range of values for an integer modulo operation of n is 0 to n − 1 ( a mod 1 is always 0; a mod 0 is undefined, being a division by zero ). When exactly one of a or n is negative, the basic definition breaks down, and programming languages differ in how these values are defined.
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 root modulo n if for every integer a coprime to n, there is some integer k for which gk ≡ a (mod n ). Such a value k is called the index or discrete logarithm of a to the base g modulo n.
Integers in the same congruence class a ≡ b (mod n) satisfy gcd(a, n) = gcd(b, n); hence one is coprime to n if and only if the other is. Thus the notion of congruence classes modulo n that are coprime to n is well-defined. Since gcd(a, n) = 1 and gcd(b, n) = 1 implies gcd(ab, n) = 1, the set of classes coprime to n is closed under ...
Primes p for which there are no solutions to H k ≡ 0 (mod p) and H k ≡ −ω p (mod p) for 1 ≤ k ≤ p−2, where H k denotes the k-th harmonic number and ω p denotes the Wolstenholme quotient.