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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 ...
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.
Indeed, a is coprime to n if and only if gcd(a, n) = 1. 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.
In mathematics, the result of the modulo operation is an equivalence class, and any member of the class may be chosen as representative; however, the usual representative is the least positive residue, the smallest non-negative integer that belongs to that class (i.e., the remainder of the Euclidean division ). [ 2]
The Higher Secondary School Certificate (HSSC), also known as Intermediate, is a public examination taken by students at Higher Secondary School or Intermediate college ( Junior college) in Pakistan. After finishing Matriculation in Grade 9 and 10, the students then enter an intermediate college and complete grades 11 and 12.
These are also class 1- primes. 2, 3, 5, 7, ... 10 p − 1 ≡ 1 (mod p 2): ... (mod p 2): 71 [20] 12 p − 1 ≡ 1 (mod p 2): 2693, 123653 ...
Reduced residue system. In mathematics, a subset R of the integers is called a reduced residue system modulo n if: gcd ( r, n) = 1 for each r in R, R contains φ ( n) elements, no two elements of R are congruent modulo n. [1] [2] Here φ denotes Euler's totient function . A reduced residue system modulo n can be formed from a complete residue ...