Ad
related to: multiplicative group modulo pdf para
Search results
Results From The WOW.Com Content Network
In modular arithmetic, the integers coprime (relatively prime) to n from the set {,, …,} of n non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n.
The group scheme of n-th roots of unity is by definition the kernel of the n-power map on the multiplicative group GL(1), considered as a group scheme.That is, for any integer n > 1 we can consider the morphism on the multiplicative group that takes n-th powers, and take an appropriate fiber product of schemes, with the morphism e that serves as the identity.
The multiplicative order of a number a modulo n is the order of a in the multiplicative group whose elements are the residues modulo n of the numbers coprime to n, and whose group operation is multiplication modulo n. This is the group of units of the ring Z n; it has φ(n) elements, φ being Euler's totient function, and is denoted as U(n) or ...
If the algebraic group is the multiplicative group mod N, the one-sided identities are recognised by computing greatest common divisors with N, and the result is the p − 1 method. If the algebraic group is the multiplicative group of a quadratic extension of N, the result is the p + 1 method; the calculation involves pairs of numbers modulo N.
That is, g is a primitive root modulo n if for every integer a coprime to n, there is some integer k for which g k ≡ a (mod n). Such a value k is called the index or discrete logarithm of a to the base g modulo n. So g is a primitive root modulo n if and only if g is a generator of the multiplicative group of integers modulo n.
Every number in a reduced residue system modulo n is a generator for the additive group of integers modulo n. A reduced residue system modulo n is a group under multiplication modulo n . If { r 1 , r 2 , ... , r φ( n ) } is a reduced residue system modulo n with n > 2, then ∑ r i ≡ 0 mod n {\displaystyle \sum r_{i}\equiv 0\!\!\!\!\mod n} .
where the modulus m is a prime number or a power of a prime number, the multiplier a is an element of high multiplicative order modulo m (e.g., a primitive root modulo n), and the seed X 0 is coprime to m. Other names are multiplicative linear congruential generator (MLCG) [2] and multiplicative congruential generator (MCG).
The modular multiplicative inverse is defined by the following rules: Existence: There exists an integer denoted a −1 such that aa −1 ≡ 1 (mod m) if and only if a is coprime with m. This integer a −1 is called a modular multiplicative inverse of a modulo m.