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This system detects all single-digit errors and around 90% [citation needed] of transposition errors. 1, 3, 7, and 9 are used because they are coprime with 10, so changing any digit changes the check digit; using a coefficient that is divisible by 2 or 5 would lose information (because 5×0 = 5×2 = 5×4 = 5×6 = 5×8 = 0 modulo 10) and thus ...
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.
The total sum of digits is 14 (0 + 2 + 2 + 1 + 4 + 5). The number that must be added to obtain the next multiple of 6 (in this case, 18) is 4. This is the resulting check code-point. The associated check character is e.
The check digit article claims that "Systems with weights ... with the weights on neighboring numbers being different, are widely used [to detect] transposition errors. 1, 3, 7, and 9 are used because they are coprime to 10, so changing any digit changes the check digit; using a coefficient that is divisible by 2 or 5 would lose information ...
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 straddling checkerboard is a device for converting an alphanumeric plaintext into digits whilst simultaneously achieving fractionation (a simple form of information diffusion) and data compression relative to other schemes using digits. It also is known as a monôme-binôme cipher.
Primitive root modulo m: A number g is a primitive root modulo m if, for every integer a coprime to m, there is an integer k such that g k ≡ a (mod m). A primitive root modulo m exists if and only if m is equal to 2, 4, p k or 2p k, where p is an odd prime number and k is a positive integer.
For any integer coprime to 10, its reciprocal is a repeating decimal without any non-recurring digits. E.g. 1 ⁄ 143 = 0. 006993 006993 006993.... While the expression of a single series with vinculum on top is adequate, the intention of the above expression is to show that the six cyclic permutations of 006993 can be obtained from this repeating decimal if we select six consecutive digits ...