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  • ...from the [[positive integer]]s to the [[complex number]]s is said to be ''multiplicative'' if <math>f(m \cdot n) = f(m) \cdot f(n)</math> for all ''[[relatively pri ...n the [[real numbers]] by <math>f(x) = x^2</math> is a simple example of a multiplicative function.
    3 KB (450 words) - 11:59, 21 July 2009
  • In Modular arithmetic, y is the multiplicative inverse of x if:
    239 bytes (40 words) - 15:46, 4 August 2021

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  • ...d the closed form for <math>\phi(n)</math> is to show that the function is multiplicative, and then breaking up <math>\phi(n)</math> into its prime factorization.
    5 KB (903 words) - 14:49, 27 July 2024
  • A (weak) '''multiplicative function''' <math>f: \mathbb{N} \to \mathbb{C}</math> is one such that <mat
    8 KB (1,401 words) - 16:49, 10 January 2025
  • is a multiplicative magic square. That is, the product of the numbers in each row, column, and
    13 KB (2,049 words) - 12:03, 19 February 2020
  • .... Using the fact that the number of divisors function <math>d(n)</math> is multiplicative, we have <math>d(n) = d(7^k)d(m) = (k+1)d(m) = 60</math>. Also, <math>d(7n)
    888 bytes (140 words) - 19:04, 24 December 2020
  • * For some <math>1\in R</math>, <math>1a=a1=a</math> (existance of multiplicative identity) Note especially that multiplicative inverses need not exist and that multiplication need not be commutative.
    6 KB (994 words) - 05:16, 8 April 2015
  • ...n <math>a \mapsto \genfrac{(}{)}{}{}{a}{p}</math> as the unique nontrivial multiplicative [[homomorphism]] of <math>\mathbb{F}_p^\times</math> into <math>\mathbb{R}^
    7 KB (1,182 words) - 15:46, 28 April 2016
  • * Scalar multiplication by the multiplicative identity of <math>F</math> is the identity transformation, so <math>\forall
    3 KB (561 words) - 23:47, 20 March 2009
  • ...ers under addition, the integers modulo <math>n</math> under addition, the multiplicative group of integers modulo <math>n</math>, and the additive group of any ring
    2 KB (346 words) - 17:30, 14 June 2020
  • ...<math>f_p</math> is equivalent to the following: "If <math>n</math> has a multiplicative [[inverse with respect to an operation | inverse]] [[mod]] <math>p</math>,
    2 KB (340 words) - 14:52, 3 April 2012
  • ...! But that is not the case. 1 over <math>x</math> is the reciprocal or the multiplicative inverse of
    2 KB (357 words) - 20:39, 16 January 2025
  • ...t also a [[complex number]] or any non-zero element of a [[field]]) is its multiplicative [[inverse with respect to an operation | inverse]]. The reciprocal is usua <math>q</math> and <math>r</math> are multiplicative inverses of each other if and only if <math>r \cdot q = q \cdot r = 1</math
    965 bytes (160 words) - 08:44, 31 December 2024
  • ...ote in particular that <math>\mathrm {Re}</math> is ''not'' in general a [[multiplicative function]], <math>\mathrm{Re}(w\cdot z) \neq \mathrm{Re}(w) \cdot \mathrm{R
    2 KB (281 words) - 14:56, 5 September 2008
  • ...Note in particular that <math>\mathrm Im</math> is ''not'' in general a [[multiplicative function]], <math>\mathrm{Im}(w\cdot z) \neq \mathrm{Im}(w) \cdot \mathrm{I
    2 KB (269 words) - 14:56, 5 September 2008
  • ...from the [[positive integer]]s to the [[complex number]]s is said to be ''multiplicative'' if <math>f(m \cdot n) = f(m) \cdot f(n)</math> for all ''[[relatively pri ...n the [[real numbers]] by <math>f(x) = x^2</math> is a simple example of a multiplicative function.
    3 KB (450 words) - 11:59, 21 July 2009
  • In [[mathematics]], a '''coefficient''' is a [[constant]] multiplicative [[divisor | factor]] of a specified object. The object can be a [[variable
    1 KB (227 words) - 21:38, 6 October 2020
  • ...0 + a = a</math> for all <math>a \in S</math>. (Existence of additive and multiplicative [[identity | identities]].) ...math> and <math>a + (-a) = (-a) + a = 0</math>. (Existence of additive and multiplicative inverses.)
    1 KB (253 words) - 18:05, 9 September 2008
  • ...' are a [[division ring]] (that is, a [[ring]] in which each element has a multiplicative [[inverse with respect to an operation | inverse]]; alternatively, a non[[c
    1 KB (157 words) - 11:29, 27 September 2024
  • ...</math>. We also note that <math> \displaystyle \tau </math> is a weak [[multiplicative function]], so for relatively prime <math> \displaystyle m,n </math>, <math
    7 KB (1,166 words) - 21:14, 10 May 2007
  • ...ce these are both [[multiplicative function]]s, <math>\psi </math> is also multiplicative, which is part (a) of the problem. For the next parts, we note that the eq Since <math>\psi </math> is multiplicative, if <math> \prod_{i=1}^k p_i^{e_i} </math> is the prime factorization of <m
    6 KB (1,007 words) - 08:10, 29 August 2011
  • ...sted in convolutions of weak [[multiplicative function]]s; the set of weak multiplicative functions is closed under convolution. In general, convolution is commutat == Closure of Weak Multiplicative Functions Under Convolution ==
    3 KB (613 words) - 20:40, 21 June 2009

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