What is Primitive: Definition and 152 Discussions

The Primitive Methodist Church is a body of Holiness Christians within the Methodist tradition, which began in England in the early 19th century, with the influence of American evangelist Lorenzo Dow (1777–1834).
In the United States, the Primitive Methodist Church had eighty-three parishes and 8,487 members in 1996. In Great Britain and Australia, the Primitive Methodist Church merged with other denominations, to form the Methodist Church of Great Britain in 1932 and the Methodist Church of Australasia in 1901. The latter subsequently merged into the Uniting Church in Australia in 1977.

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  1. C

    Algebra help - primitive roots and minimal polynomials

    Homework Statement (a) Find a primitive root β of F3[x]/(x^2 + 1). (b) Find the minimal polynomial p(x) of β in F3[x]. (c) Show that F3[x]/(x^2 + 1) is isomorphic to F3[x]/(p(x)). The Attempt at a Solution I am completely lost on this one :confused:
  2. A

    Why set is taken as undefined primitive?

    the title says everything. why they don't define set? is it possible to do so? if not, why?
  3. M

    What is exact reason behind choosing basic primitive shapes for elements in FEA?

    what is exact reason behind choosing basic primitive shapes for elements in FEA? Why it can't be hexagonal, pentagonal, octagonal, etc. in both cases 2D and 3D... Thanks in advance...
  4. L

    Designing a Two-Bit Adder Using Verilog Primitive Gates

    designing a two-bit adder using verilog's primitive gates_I get "z" for my outputs Hi, I am trying to write verilog code for a two bit adder using verilog's primitive gates. I had implemented a two bit adder before...using gates I myself had implemented with nmos and pmos transistors, with...
  5. G

    Proof Two Primitive Root Conditions Are Equivalent

    Homework Statement Let n be a nonzero integer and let a be an integer with gcd(a, n) = 1. We have two equivalent conditions which characterize primitive roots: (i) a is primitive modulo n if the order of a is \phi(n). (ii) a is primitive modulo n if for every element b with gcd(b, n) = 1 we...
  6. K

    Primitive Pyth. triples: Solutions of x^2 + y^2 = 2 z^2

    Theorem: The positive primitive solutions of x^2 + y^2 = z^2 with y even are x = r^2 - s^2, y = 2rs, z = r^2 + s^2, where r and s are arbitrary integers of opposite parity with r>s>0 and gcd(r,s)=1. Using this theorem, find all solutions of the equation x^2 + y^2 = 2z^2 (hint: write the...
  7. K

    What Defines a Primitive Pythagorean Triple?

    Definition: A primitive Pythagorean triple is a triple of natural numbers x,y,z s.t. x^2 + y^2 = z^2 and gcd(x,y,z)=1. note: d|gcd(x,y) => d|x and d|y => d^2|x^2 and d^2|y^2 Now z^2 = x^2 + y^2 => d^2|z^2 => d|z Thus, it follows that for any Pythagorean triple x,y,z, we must have...
  8. K

    Primitive roots & Reduced residue system

    Let p be a prime. a) If gcd(k,p-1)=1, then 1^k, 2^k,..., (p - 1)^k form a reduced residue system mod p. b) If 1^k, 2^k,..., (p - 1)^k form a reduced residue system mod p, then gcd(k,p-1)=1. ================================= I proved part a by first showing that each of 1^k, 2^k,..., (p -...
  9. G

    Rhombohedral primitive cell on FCC

    How do you determine a plane or a point on a crystal lattice when translated to a rhomboidal primitive cell. For example, rhombohedral primitive cell for an FCC is defined as: a_1 = 1/2 a*(x+y); a_2=1/2*a(y+z); a_3=1/2*a(z+x); If we have a plane, for example the 111 plane on an FCC, how...
  10. T

    Number theory: primitive roots

    Find a primitive root modulo 101. What integers mod 101 are 5th powers? 7th powers? -I tested 2. -2 and 5 are the prime factors dividing phi(101)=100 so i calculated 2^50 is not congruent to 1 mod 101 and 2^20 is not congruent to 1 mod 101. -Therefore 2 is a primitive root modulo 101 I guess...
  11. J

    Primitive Roots helping please

    Please prove that if x is quadratic nonResidue modulo 109 and x also cubic nonresidue modulo 109 than x is guaranteed to be primitive root modulo 109 thanks you very much
  12. H

    Is α a Primitive Element Modulo p Given α^q ≡ -1 mod p?

    Suppose that p and q are odd primes and p=2q+1. Suppose that α∈ Z_p^*,α≢±1 mod p. Prove that α is primitive element modulo p if and only if α^q≡-1 mod q.
  13. D

    Strongly connected primitive matrix

    If H is a nxn primitive, irreducible matrix, is it always true that Hn-1 > 0? That is, every entry in Hn-1 is positive. From my class notes, the definition of H primitive is that there exists some k>0 such that Hk > 0. And a matrix is irreducible if its digraph is strongly connected (that...
  14. T

    Relationship between primitive roots of a prime

    Hi all, I've been staring at this question on and off for about a month: Suppose that p is an odd prime, and g and h are primitive roots modulo p. If a is an integer, then there are positive integers s and t such that a \equiv g^s \equiv h^t mod p. Show that s \equiv t mod 2. I feel as...
  15. J

    Finite Field Elements: F2n (1-8)

    Give one primitive element for each of the finite field: F2n (here "2" is the subscript) for n=1, n=2,...,n=8
  16. Loren Booda

    Can a primitive galaxy nova or supernova?

    Can a primitive galaxy nova or supernova? Might the former process be involved with star production or the latter with a quasar?
  17. B

    Solved: Help with Primitive Calculus Problem

    Help in a primitive! Homework Statement Hello guys! Please, I'm really needing help in a primitive... I don't know, maybe it has a simple solution, but I'm tired and blocked on this... Can you give some lights? Here goes the equation: \int\frac{dx}{x^{2}\sqrt{4-x^{2}}} Homework...
  18. S

    Is there a simple way to determine if an element is a primitive root modulo n?

    Is there an easy (by which I mean an algorithm polynomial in size of input) way to know whether in the multiplicative group of integers mod P (P is a prime), whether an element is a generator or not?
  19. B

    Primitive Matrix: Is M^k Positive?

    Hi All, I have the following matrix M = M_1 M_2 M_3 ... M_n M is then a product of n matrices. Each of those has dimension 2n by 2n and has the same "look". Consider M_n: this matrix is equal to the identity matrix, 2n by 2n. The only thing different from the identity is that the 3 by 3...
  20. R

    An odd question (relationship between derivative and primitive)

    Is there an explicit formula for finding the antiderivative of a function? I was thinking that perhaps it would be the inverse function of the derivative, but I don't know what that would be off the top of my head.
  21. H

    Proving the Primality of a Polynomial over Finite Fields

    Let f = X^n + a_{n-1}X^{n-1} + \cdots + a_1X + a_o be a polynomial over \mathbb{F}_q for some prime power q such that the least common multiple of the (multiplicative) orders of its roots (in \mathbb{F}_{q^n}) is q^n -1. I would like to show that one of these roots has order q^n -1. (I.e. the...
  22. M

    Primitive 5th root of unity extension

    Hi, Let E = Q(a), where a is a primitive fifth root of unity. Find a basis for E as a vector space over Q, and express a/a-3 in terms of this basis. I can find a basis for E: {1, a, a^2, a^3}, but am not sure how to express a/a-3 in terms of this basis. Any help much appreciated.
  23. T

    Finding the Number of Primitive Polynomials in Finite Fields

    Can anyone tell me how to find the exact number of primitive polynomials of degree n over a finite field F_q? I believe the answer is φ(q^n-1)/n, but I cannot find a proof of this. Thanx in advance.
  24. R

    Primitive roots - annoying problem

    Let r be a primitive root of a prime number p \geq 3. Prove that if p \equiv 1 (mod 4), then -r is also a primitive root of p. I've been told it's quite easy, but I can't see why it's true for the life of me :frown:
  25. S

    Artin's Conjecture on Primitive Roots: Perfect Squares

    If a is a perfect square then a is not a primitive root modulo p (p is an odd prime). (from Artin's conjecture on primitive roots) http://en.wikipedia.org/wiki/Artin%27s_conjecture_on_primitive_roots This is what I know: suppose a = b^2 a is a primitive root mod p when , a^(p-1) congruent to 1...
  26. D

    How do I find the reciprocal primitive vector for a lattice?

    Homework Statement Here's a problem I'm having: The primitive vectors of the hexagonal lattice are: a1 = ck a2 = (a/2)i + ([a√3]/2)j a3 = (-a/2)i + ([a√3]/2)j Find the primitive vectors of the reciprocal lattice, i.e. b1, b2, and b3. Homework Equations I do know that the...
  27. S

    Solving Number Theory Problems: Totient & Primitive Roots

    Homework Statement Hi guys, i have never taken number theory yet now I am forced to quickly understand it as it was required for a class i signed up. I need help with these problems and would greatly appreciate any hints or help in the right direction. Thanks. 1)Find with proof, all n such...
  28. E

    Mathematical Definition of a Primitive Cell

    [SOLVED] primitive cell Homework Statement http://en.wikipedia.org/wiki/Primitive_cell Could someone give me a mathematically rigorous of a primitive cell? I have read like 4 different definitions and none of them seem mathematically rigorous. I think Wikipedia's definition is particularly...
  29. A

    What is the coordination number of an atom in a primitive cubic struct

    I don't understand this question at all. But since my Professor gave it to me I'm guessing it relates to the chapter of structures and types of solids. What is the coordination number of an atom in a primitive cubic structure? What the hell is this question asking for?
  30. T

    Multiplication of primitive roots

    Hi I noticed that multiplication of all primitive roots modulo p ,p>3, congruent to 1 modulo p... I have tried some examples (13,17,19...) but i couldn't prove the general case (let g1...gk be primitive roots modulo p,p>3 ==> g1*g2*...*gk=1(p)) I need help to prove or disprove...
  31. mattmns

    Number Theory - Primitive Roots

    Here is the question: ----------- Suppose n has a primitive root g. For which values of a (in terms of the primitive root g) does the equations x^2 \equiv a \ \text{(mod n)} have solutions? ----------- I really don't have much of an idea of how to even begin this one. Let g be a primitive...
  32. mattmns

    Number Theory - Primitive Roots

    Here is the question from the book: ------------ Determine a primitive root modulo 19, and use it to find all the primitive roots. ------------ \varphi(19)= 18 And 18 is the order of 2 modulo 19, so 2 is a primitive root modulo 19, but I am not sure of how to use that to find all...
  33. N

    Show Primitive Roots Cannot be Perfect Cubes Modulo Prime p

    If a is a perfect cube, a= n^3, for some integer n, and p is a prime with p is congreunt to 1 mod 3, then show that a cannot be a primitive root mod p, tat is ep(a) is not equal to p - 1
  34. E

    Solving a Diff. Eq. Involving Primitive of sen x^3

    Homework Statement I'm stuck trying to solve a differential equation at the point i need to calculate the primitive of sen x^3 Homework Equations The Attempt at a Solution I've thought on primitives by parts but I don't know how will I do it...
  35. X

    Cyclotomic polynomials and primitive roots of unity

    w_{n} is primitive root of unity of order n, w_{m} is primitive root of unity of order m, all primitve roots of unity of order n are roots of Cyclotomic polynomials phi_{n}(x) which is a minimal polynomial of all primitive roots of unity of order n , similarly, phi_{m}(y) is a minimal...
  36. S

    Roots Of Unity - Is It Primitive?

    All right, thanks to everybody's help, I've got the algorithm for determining the nth roots of unity. However, for determining which ones are primitive, I'm still having a little trouble. If n is odd, I can test if (n, k) are coprime. However, for even values of n, it seems that it doesn't...
  37. E

    Primitive of x/sqrt(4+x^4): Is Substitution Necessary?

    I know that tu solve this primitive we have tu use the substitution method,but I think that none of the rules that should be used apply to this!The problem is, to use the substitution: x=a/b sen t we should have the function in the format (sqrt(a^2 - b^2*x^2)),but instead of a x^2 I have a x^4...
  38. S

    Discrete Weighted Transform - A Primitive Nth Root of Unity

    Hello, I got pointed to this forum by OfficeShreder. I have a question I've been puzzling myself over for a while. I am currently trying to implement the "Discrete Weighted Transform". I have reached a step where I need to determine "a primitive Nth root of unity in the appropriate domain"...
  39. B

    Primitive Roots: Exploring Their Significance and Finding Them

    I was curious why primitive roots are so important? Also, how one would find out if a number has a primitive root and what and how many of them they are?
  40. D

    Counting Primitive Roots in Finite Fields without Group Theory

    I have the definition that if F is a finite field then a \in F is a primitive root if ord(a) = |F|-1. Now what I don't understand is how exactly are there \phi(|F|-1) primitive roots? (Note: This material is supposed not to use any group theory.)
  41. A

    Crystal Structure: Primitive base vectors etc

    This is the question: http://www.maths.tcd.ie/~cockburd/Question.jpg It's not a homework question, merely one from a previous years tutorial sheet. Okay so it's tetragonal conventional unit cell, has a sort of face centered structure right? Em.. so that would mean it has a four point basis...
  42. P

    Find Primitive Root Modulo 125 - The Easier Way

    How would I go about finding a number that is a primitive root modulo 125? There definitely exists a primitive root since 5^3 =125 The problem basically comes down to finding 'a' (primitive root); a^50 congruent to -1 (mod 125) Anyone know a way apart from trial and error? Thanks
  43. H

    Primitive variables in Fluid Mechanics

    Hello! I know that the primitive variables in fluid mechanics are velocity and pressure. But why? I don't see how "primitive" these variables are...What does it mean by a "primitive variable"? Is that all other variables in a fluid flow can be derived from velocity and pressure? Is there any...
  44. P

    Primitive Roots: Multiple Possibilities?

    Can a number have more than 1 primitive root? Thanks
  45. T

    Primitive Function: Finding the Right Direction

    Hi, I don't know how to find this primitive function: \int \frac{dx}{(1+\tan x)(1+\tan^2 x)} I tried substitutions t = \tan x or t = 1 + \tan x, but it didn't seem to help me lot... Could someone please point me to the right direction? Thank you.
  46. M

    Primitive polynomial in GF(4) ?

    primitive polynomial in GF(4) ?? Hai All, I m required to make a pseudo random generator. I know that i can make that using some Flip flops and XOR gates(in linear feedback shift register configuration ). But the resulting PN sequences will be in Galois Field(2) as the taps for the flip...
  47. K

    Primitive of Arctan x: Ideas & Solutions

    Please any idea on this,find the primitive of arctan x
  48. N

    Primitive recursive functions :mad:

    Let f be a primitive recursive total function, and let A be the set of all n such that the value f(n) is 'new' in the sense of being different from f(m) for all m<n. Show that A is primitive recursive. How in the world do I attack this problem? I am totally lost. Any help would be greatly...
  49. A

    Primitive roots, specifically of 18

    this problem is annoying. I've found that the primitive roots of 9 are 2 and 5. since 2|18 it can't be a root. i know via some theorems in my book that if 5 is a primitive root of 3, then its a primitive root of 3^k, and also of 2*3^k. sorry about not using latex, shouldn't need it for...
  50. G

    Primitive Recursive Proof in Davis, Sigal & Weyuker Textbook

    In the Davis, Sigal & Weyuker textbook "Computability, Complexity and Languages" their proof that f(x) = x + y goes like this: \begin{equation*}\begin{split}f(x,0) &= u_1^1(x)\\f(x,y+1) &= g(y,f(x,y),x)\end{split}\end{equation*} where g(x_1,x_2,x_3) = s(u_2^3(x_1,x_2,x_3)). And (I'm...
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