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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.
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.
A residue numeral system (RNS) is a numeral system representing integers by their values modulo several pairwise coprime integers called the moduli. This representation is allowed by the Chinese remainder theorem, which asserts that, if M is the product of the moduli, there is, in an interval of length M, exactly one integer having any given set of modular values.
Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, [1] and more generally, fixed point binary values. Two's complement uses the binary digit with the greatest value as the sign to indicate whether the binary number is positive or negative; when the most significant bit is 1 the number is signed as negative and when the most ...
Modular exponentiation can be performed with a negative exponent e by finding the modular multiplicative inverse d of b modulo m using the extended Euclidean algorithm. That is: c = be 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.
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.
Most commonly, the modulus is chosen as a prime number, making the choice of a coprime seed trivial (any 0 < X 0 < m will do). This produces the best-quality output, but introduces some implementation complexity, and the range of the output is unlikely to match the desired application; converting to the desired range requires an additional multiplication.
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