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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]
The Luhn mod N algorithm is an extension to the Luhn algorithm (also known as mod 10 algorithm) that allows it to work with sequences of values in any even-numbered base. This can be useful when a check digit is required to validate an identification string composed of letters, a combination of letters and digits or any arbitrary set of N ...
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 ...
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.
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.
Integer multiplication respects the congruence classes, that is, a ≡ a' and b ≡ b' (mod n) implies ab ≡ a'b' (mod n). This implies that the multiplication is associative, commutative, and that the class of 1 is the unique multiplicative identity. Finally, given a, the multiplicative inverse of a modulo n is an integer x satisfying ax ≡ ...
If the remainder is equal to 0 then use 0 as the check digit, and if not 0 subtract the remainder from 10 to derive the check digit. A GS1 check digit calculator and detailed documentation is online at GS1's website. [5] Another official calculator page shows that the mechanism for GTIN-13 is the same for Global Location Number/GLN. [6]
Using the extended Euclidean algorithm, compute −5 ⋅ 10 + 3 ⋅ 17 = 1, so N′ will be −3 mod 10 = 7. The Montgomery forms of 7 and 15 are 70 mod 17 = 2 and 150 mod 17 = 14, respectively. Their product 28 is the input T to REDC, and since 28 < RN = 170, the assumptions of REDC are satisfied. To run REDC, set m to (28 mod 10) ⋅ 7 mod 10 ...