An nth root of unity ε is an element such that en-1. We say that ε is primitive if every nth root of unity is ek for some k. Show that there is przmatwe if every nth root of unity 1s * for k some are primitive nth roots of unity En E C for all n, and find the degree of QQ(En) for 1 < n <6

Q: Compute the coefficent of x8    in the expansion of (3x -2)13

A: The given expression is,

Q: Abstract Algebra: Assist me please.

A: To prove that the kernel of a group homomorphism is always a normal subgroup of the domain (group)

Q: Abstract algebra (proof writing):

A: To analyze the group structure of G/H , G , H as given

Q: I do not understand number 8. Can you explain me how to do it?  Thank you.

A: As per norms, the three parts f, g and h are answered. Questions regarding relations and functions

Q: Show that if E is an algebraic extension of a field F and contains all zeros in \bar{F} of every  f ...

A: To show:  

Q: Abstract Algebra (Proof writing): Looking for assistance on this problem.

A: Consider the function φ:Z/6Z -&gt;Z6  ,

Q: The differential equation for a freee-falling mass m near the surface of the earth is given by:  d2s...

A: Consider the equation:

Q: Comlex Analysis, only need part d.

A: The function is

Q: rewrite the function F = (A ⊕ B) ⊕ C without the XOR operator, ⊕.

A: The given function is F = (A ⊕ B) ⊕ C.

Q: Question attached in photo

A: To verify the given equality regarding the limit of f(z) (z a complex variable)

Q: Solve the linear system by the Gauss Jordan Elimination Method: 4x - 4y + 4z = -8 x - 2y - 2z = -1 2...

A: To bring (reduce) the given system of equations to triangular form and then to diagonal form  and th...

Q: prove in a field with four elements, F = {0,1,a,b}, that 1 + 1 = 0.

A: The given four elements are F = {0, 1, a, b}.Consider ab belongs to F and then there are four possib...

Q: Abstract Algebra   The problem and D3 is given in the below picture.

A:

Q: Differential equations Consider the vectors x1(t) and x2(t) Please refer to attached image for vecto...

A: Obtain the Wronskian of the vectors as follows.

Q: 0, 2 is defined by A natural cubic spline S on 5. So()12x - 0 if 1 (1) S(r)2b(x1)c(x - 1)2d(x - 1) i...

A: 5.Note that, the natural cubic spline must satisfy the conditions

Q: Prove that if p is a prime, then the square root of p is irrational.

A:

Q: Suppose f(z) is analytic for |z| &lt;= 1, and |f(z)| &gt;=1. If f(0) =1, prove that f(z) is constant...

A: To prove that the given conditions on the analytic function force it to be the constant function f(z...

Q: I need you to solve question no 5 only

A: To prove that the volume of a rectangular solid under the given conditions attains its maximum when ...

Q: Determine a lower bound for the radius of convergence of series solutions about the given point x0 f...

A: Given:The differential equation is (x2-2x-3)y”+xy’+4y=0

Q: 4. Suppose that (X, dx) and (Y, dy) are metric spaces, and define distance on X × Y by Prove that (T...

A: Hey, since there are multiple questions posted, we will answer first question. If you want any speci...

Q: 5.2.6.C          Discrete Mathematics This is a dublicate please answer the question as quickly as p...

A: Known fact:Proof for strong induction hypothesis.Base: Show that P(1) is true.Induction: If P(1) and...

Q: How many possible graphs can be created on 5 distinct vertices?

A: Consider a graph of n vertices.The line connecting any two vertices of a graph is called as an edge ...

Q: pls explain to me step by step. thanks

A: To exponentiate the matrix tA, A as given, using the special properties of A.

Q: Abstract Algebra: Its a part 1 and 2 problem. Definitions are provided. I need some help on this pro...

A: To understand homomorphism from quotient groups

Q: 4. How many permutations of the letters ABCDEFG contain: a) the string GD? b) the string AFC? c) the...

A: (a) The number of permutations of the letters ABCDEFG that contains the string GD.There are 7 letter...

Q: 6.3.16 How many subsets with an odd number of elements does a set with 10 elements have?

A: Consider that the set has 10 elements and we need to find the subsets with an odd number of elements...

Q: I needed help solving this problem. Thank you.

A: Hey, since there are multiple subparts posted, we will answer first 3 questions. If you want any spe...

Q: Abstract Algebra

A: To define the concept of a subfield of a field and prove the stated property regarding subfields of ...

Q: Laplace transform Evaluate (please see image)

A: Given:

Q: Solve the differential equation using either the method of undetermined coefficients or Laplace tran...

A: The differential equation is y′″ -6y″+11y′-6y = 3x.

Q: Abstract Algebra

A: To find the smallest degree polynomial f(x) with coefficients in Q, such that f(√2+√3)=0.

Q: Solve the initial value problem using the method of undetermined coefficients. y"+4y'+4y=(3+x)e-2x, ...

A: Consider the given initial value problem:

Q: Z is a complex variable z=x+iy  question attached as photo

A: The area enclosed by a simple closed curve,

Q: Find the differential equation whose general solution is y=c1e4t+c2e-5t

A: Find the differential equation of given solution.

Q: 9. A manufacturer wants to layout the parts on a sheet of steel in 14 rows and 6 columns with a spac...

A: Given: 14-rows6-columnsSpace=1/2 between each row and column.First, we calculate the width of the sm...

Q: 5.2.6          Discrete Mathematics (I filled in as much as I could) A) determine which amounts of ...

A: (A)We are given that the postage can be formed by using the stamps of just 3-cent and 10-cent only,S...

Q: 27 Compute the simple dijuctive sum, disjoin sum, simple diniene. and bounded difference of the sets...

A: The two sets are given by,

Q: Is multiplication modulo 6 a binary operation on Z6^*? why or why not?

A: Take two elements in the set.Check whether multiplication modulo 6 of two elements is again in the s...

Q: I need help with this question. Thanks!

A: Hey, since there are multiple questions posted, we will answer first question. If you want any speci...

Q: 14. A stair stringer is to be cut to reach a 2nd story floor in a house with nine foot ceilings. The...

A: The total rise is 106 inches.Let x be the number of rises and y be the actual rise height.Since all ...

Q: a fair coin is tossed three times. what is the probability of obtaining at least two tails?

A: Let S be the number of outcomes when the coin tossed three times and A be the possibilities to get a...

Q: Find the first five nonzero terms in the solution to the initial value problem: y"-2xy'+8y=0, y(0)=3...

A:

Q: of 2 3. If you read 20 books this year, a. How many different sets of 6 books could you recommend so...

A: Total number of books read this year, n = 20(a) To find the number of different sets of 6 books that...

Q: 1. How many bitstrings of length 10 are there: a. with no restrictions? b. start with 11 or end with...

A: (i) The number of bitstrings of length 10 that can be obtained when no restriction is laid.Since eac...

Q: All the students in the sixth grade either purchased their lunch or brought their lunch 15 from home...

A: Let x be the number of students in the sixth grade.Given condition: Either the student purchased the...

Q: Abstract Algebra. Please explain everything in detail.

A: To discuss the reason why the three given functions fail to satisfy the properties of a Euclidean no...

Q: pls explain to me step by step. thanks

A: To establish the (given) necessary and sufficient conditions for the periodicity of solutions of the...

Q: Assume that you are located at (A) which is New Orleans. Let Boston (B), Chicago (C) , Denver (D), a...

A: Solution contextSince the data about the distances between the cities, modes of transport or transpo...

Q: Hello, I need help with this question. Thanks!

A: Let us assume the number of hours per week, the first mine is operated is x and the number of hours ...

Q: the book is "First Course on Fuzzy Theory and Applications"

A: To show that the given assignment f(tilda) is a fuzzifying function

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.