the multiplicative order of a modulo n is the order of a in the multiplicative group of the units in the ring of the integers modulo n. The order of a...

Multiplicative may refer to: Multiplication Multiplicative function Multiplicative group Multiplicative identity Multiplicative inverse Multiplicative...

is replaced with multiplication by the reciprocal (multiplicative inverse) then the associative and commutative laws of multiplication allow the factors...

the multiplicative order modulo a prime number. More precisely, given a prime number p and an integer b coprime with p, the multiplicative order of b...

generalizations See Multiplication in group theory, above, and multiplicative group, which for example includes matrix multiplication. A very general, and...

coprime. An arithmetic function is said to be completely multiplicative (or totally multiplicative) if f ( 1 ) = 1 {\displaystyle f(1)=1} and f ( a b ) =...

{\text{ if and only if }}{\text{ ord}}(a)|(n-1).} Therefore, the multiplicative order of 17 (mod 71) is not necessarily 70 because some factor of 70 may...

products are important and are called completely multiplicative functions or totally multiplicative functions. A weaker condition is also important, respecting...

of its monomials; the multiplicative order, that is, the number of times the polynomial is divisible by some value; the order of the polynomial considered...

mathematics and group theory, the term multiplicative group refers to one of the following concepts: the group under multiplication of the invertible elements of...

classes modulo n. As explained in the article multiplicative group of integers modulo n, this multiplicative group ( Z {\displaystyle \mathbb {Z} } × n)...

on the integers modulo the multiplicative order of α {\displaystyle \alpha } , and takes values in the same set. In order to describe every element, it...

approximation in Big O notation Z-order (curve), a space-filling curve Multiplicative order in modular arithmetic Order of operations Orders of magnitude...

_{\ell =1}^{k-1}N_{\ell }\right)n_{k}} where the empty product is the multiplicative identity element, i.e., ∏ ℓ = 1 0 N ℓ = ∏ ℓ = d + 1 d N ℓ = 1 {\textstyle...

the multiplication is associative, commutative, and that the class of 1 is the unique multiplicative identity. Finally, given a, the multiplicative inverse...

same complexity as matrix multiplication (up to a multiplicative constant), the computational complexity of matrix multiplication appears throughout numerical...

solution, i.e., when it exists, a modular multiplicative inverse is unique: If b and b' are both modular multiplicative inverses of a respect to the modulus...

the first column since 1 is the multiplicative identity.[citation needed] The traditional rote learning of multiplication was based on memorization of columns...

applying the mathematical definition of matrix multiplication gives an algorithm that takes time on the order of n3 field operations to multiply two n × n...

Select an element g ∈ F p ∗ {\displaystyle {\mathbb {F} _{p}}^{*}} of multiplicative order l. Then for each (n+1)-dimensional vector a = (a0,a1, ..., an)∈ (...

p − 1 digits if and only if p is a full reptend prime. That is, the multiplicative order ordp b = p − 1, which is equivalent to b being a primitive root modulo...

{\displaystyle a} is contained in the multiplicative group of integers modulo N {\displaystyle N} , having a multiplicative inverse modulo N {\displaystyle...

subject. The Mathematics Subject Classification for multiplicative number theory is 11Nxx. Multiplicative number theory deals primarily in asymptotic estimates...

Sometimes these are called inverse powers of two because each is the multiplicative inverse of a positive power of two. Because two is the base of the binary...

element of high multiplicative order modulo m (e.g., a primitive root modulo n), and the seed X0 is coprime to m. Other names are multiplicative linear congruential...

modulo p under multiplication, which has order p − 1. Notice that 2 (strictly speaking, its image modulo p) has multiplicative order equal to 2 n + 1...

for multiplication-respecting order relations on the set of monomials that are not well-orders. In the case of finitely many variables, well-ordering of...

matrices of order n is an example of an associative algebra over the field of real numbers under matrix addition and matrix multiplication since matrix...

transient of ⁠1/k⁠ is max(a, b), and the period equals r, where r is the multiplicative order of 10 mod n, that is the smallest integer such that 10r ≡ 1 (mod...

or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication, the order of an element a of...