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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.
Consequently, (a mod m) denotes generally the unique integer k such that 0 ≤ k < m and k ≡ a (mod m); it is called the residue of a modulo m. In particular, (a mod m) = (b mod m) is equivalent to a ≡ b (mod m), and this explains why "=" is often used instead of "≡" in this context.
c = b e mod m = d −e mod m, where e < 0 and b ⋅ d ≡ 1 (mod m). Modular exponentiation is efficient to compute, even for very large integers. On the other hand, computing the modular discrete logarithm – that is, finding the exponent e when given b , c , and m – is believed to be difficult.
Different programming languages have adopted different conventions. For example: Pascal chooses the result of the mod operation positive, but does not allow d to be negative or zero (so, a = (a div d) × d + a mod d is not always valid). [4] C99 chooses the remainder with the same sign as the dividend a. [5] (Before C99, the C language allowed ...
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.
DHTML (Dynamic HTML) allows scripting languages, such as JavaScript, to modify variables and elements in a web page's structure, which in turn affect the look, behavior, and functionality of otherwise "static" HTML content after the page has been fully loaded and during the viewing process.
Another example is the Ajax programming technique, where, for example, clicking a hypertext link may cause JavaScript code to retrieve the text for a new price quotation to display in place of the current one within the page, without re-loading the whole page. When the new text arrives back from the server, the JavaScript must identify the ...
The register width of a processor determines the range of values that can be represented in its registers. Though the vast majority of computers can perform multiple-precision arithmetic on operands in memory, allowing numbers to be arbitrarily long and overflow to be avoided, the register width limits the sizes of numbers that can be operated on (e.g., added or subtracted) using a single ...