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Scheme offer two functions, remainder and modulo – Ada and PL/I have mod and rem, while Fortran has mod and modulo; in each case, the former agrees in sign with the dividend, and the latter with the divisor. Common Lisp and Haskell also have mod and rem, but mod uses the sign of the divisor and rem uses the sign of the dividend.
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.
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.
The rem and millirem are CGS units in widest use among the U.S. public, industry, and government. [4] However, the SI unit the sievert (Sv) is the normal unit outside the United States, and is increasingly encountered within the US in academic, scientific, and engineering environments, and have now virtually replaced the rem. [5]
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