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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]
Modulo is a mathematical jargon that was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. [3] Given the integers a, b and n, the expression "a ≡ b (mod n)", pronounced "a is congruent to b modulo n", means that a − b is an integer multiple of n, or equivalently, a and b both share the same remainder when divided by n.
and −2 is the least absolute remainder. In the division of 42 by 5, we have: 42 = 8 × 5 + 2, and since 2 < 5/2, 2 is both the least positive remainder and the least absolute remainder. In these examples, the (negative) least absolute remainder is obtained from the least positive remainder by subtracting 5, which is d. This holds in general.
The Mathematical Alphanumeric Symbols block (U+1D400–U+1D7FF) contains Latin and Greek letters and decimal digits that enable mathematicians to denote different notions with different letter styles. The reserved code points (the "holes") in the alphabetic ranges up to U+1D551 duplicate characters in the Letterlike Symbols block. In order ...
The block length of a block code is the number of symbols in a block. Hence, the elements c {\displaystyle c} of Σ n {\displaystyle \Sigma ^{n}} are strings of length n {\displaystyle n} and correspond to blocks that may be received by the receiver.
The styled characters are mostly located in the Mathematical Alphanumeric Symbols block, but the 24 characters in cells with a pink background are located in the letterlike symbols block, for example, ℛ (script capital r) is at U+211B rather than the expected U+1D4AD which is reserved.
The division with remainder or Euclidean division of two natural numbers provides an integer quotient, which is the number of times the second number is completely contained in the first number, and a remainder, which is the part of the first number that remains, when in the course of computing the quotient, no further full chunk of the size of ...
A block is a grouping of code that is treated collectively. Many block syntaxes can consist of any number of items (statements, expressions or other units of code) – including one or zero. Languages delimit a block in a variety of ways – some via marking text and others by relative formatting such as levels of indentation.