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...

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 ) =...

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...

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

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

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

{\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...

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

converse is also true: 2pk ≡ 2 (mod p2) for some k ≥ 1 implies that the multiplicative order of 2 modulo p2 divides gcd(pk − 1, φ(p2)) = p − 1, that is, 2p−1 ≡ 1 (mod p2)...

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

_{\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...

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

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...

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

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...

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

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...

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...

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

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...

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...

to return a deck of cards of even size n, to original order is given by the multiplicative order of 2 modulo (n + 1). For example, for a deck size of n=2...

have a special form. The Lucas test relies on the fact that the multiplicative order of a number a modulo n is n − 1 for a prime n when a is a primitive...

class of all ordinal numbers ord(V), the order type of a well-ordered set V ordn(a), the multiplicative order of a modulo n Ord Publishing, an imprint...

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...

lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences...