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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.
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.
MATLAB (an abbreviation of "MATrix LABoratory" [22]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
If a ≡ b (mod m), then it is generally false that k a ≡ k b (mod m). However, the following is true: If c ≡ d (mod φ(m)), where φ is Euler's totient function, then a c ≡ a d (mod m) —provided that a is coprime with m. For cancellation of common terms, we have the following rules: If a + k ≡ b + k (mod m), where k is any integer ...
For a given positive integer m, two integers, a and b, are said to be congruent modulo m if m divides their difference. This binary relation is denoted by, ().This is an equivalence relation on the set of integers, , and the equivalence classes are called congruence classes modulo m or residue classes modulo m.
Custom Function @PowerMod() for FileMaker Pro (with 1024-bit RSA encryption example) Ruby's openssl package has the OpenSSL::BN#mod_exp method to perform modular exponentiation. The HP Prime Calculator has the CAS.powmod() function [permanent dead link ] to perform modular exponentiation. For a^b mod c, a can be no larger than 1 EE 12.
output: Integer S in the range [0, N − 1] such that S ≡ TR −1 mod N m ← ((T mod R)N′) mod R t ← (T + mN) / R if t ≥ N then return t − N else return t end if end function To see that this algorithm is correct, first observe that m is chosen precisely so that T + mN is divisible by R .
In mathematics, the sign function or signum function (from signum, Latin for "sign") is a function that has the value −1, +1 or 0 according to whether the sign of a given real number is positive or negative, or the given number is itself zero.