Please see the attached file for the fully formatted problems.
Problem #4 A palindromic polynomial is such that for all . Now we use the result in problem #3 to find an irreducible palindromic polynomial of degree 6 over . First, we compute all reducible ones. Now we consider the palindromic . From problem #3(c), is irreducible. I am sorry but I do not understand the definit
Show that if a palindromic polynomial of degree n is irreducible over F, then n must be even. Hint Experiment with palindromic polynomials of odd degree Please, can you explain what does palindromic polynomials means? Give me examples palindromic polynomials with even and odd degree.
Find the polynomials that represent 1/x^3+x , x/x^3+x, x^2/x^3+x, and x^3/x^3+x modulo the irrreducible polynomial x^5+x^2+1 over F2 ( the field with two elements 0 and 1) Your answers should be polynomials over F2 with degrees at most four. (Can you explain in here why at most degree four) Note: Use the Eucliden algorith
Show that if the roots of the polynomial p are all real, then the roots of p' are all real. If, in addition, the roots of p are all simple, then the roots of p' are all simple.
(1) You are having a meeting with the employees of Financial Outsourcing, Inc. During the meeting, you were asked several questions. Give your opinion to the questions. - Why do you think the Federal government adjusts (raises or lowers) the prime interest rate? - What do you think are some of the effects of the adjustmen
Prime number factorization Express 45 as a product of prime numbers
Problem 1: Prove that there are no integers x, y, and z such that x^2 +y^2 + z^2 = 999 Problem 2: Show that square root of 2 cubed is an irrational number. Problem 3: For each of the following pairs a and b, use the division algorithm to find quotient q and remainder r. (a) b=189, a=17
#1: f(x)=(1x^3-18x^2+101x-168)/(1x^3-2x^2-41x+42) Find: All Roots:? All Holes:? All Vertical Asymptotes:? The answer to the 1st question is NOT 8 or -8. #2: f(x)= (-2x^3+37x^2-222x+432)/(1x^3+3x^2-64x-192) I need the roots: (I have two of them (9/2) and (6) but I need the third)? I need to know the hol
Section 4.3 Collect like terms. 4 4 52. 3a - 2a + 2a + a Collect like terms and then arrange in descending order. 3 3 4 66. -1 + 5x - 3 - 7x + x + 5 Classify the polynomial as a monomial, binomial, trinomial, or none o
Prove that (Fn+1)^2 - Fn Fn+2 = (- 1)^n
Suppose that F1 = 1, F2 = 1, F3 =1, F4 = 3, F5 = 5, and in general Fn = Fn-1 + Fn-2 for n ≥ 3 ( Fn is called the nth Fibonacci number.) Prove that F1 + F2 + F3 +...+ Fn = F(n + 2) - 1
Prove that there are no integers x, y, and z such that x^2 + y^2 + z^2 = 999.
List all irreducible polynomial of degree 2, 3 and 4 over F22juu2332. Prove your assertion. Please see the attached file for the fully formatted problems.
1) How do I show x+1 is primitive? 2) How do I prove x^4+x^3+1 is an irreducible polynomial of degree 4 over Z mod?
17. The first three Legendre polynomials are P0(x) =1 , P1(x) = x and P2(x)=1/2(3x^2-1). If x = cos θ, then P0(cos θ)=1 and P1(cos θ)= cos θ. Show that p2(cos θ)= 1/4(3 cos 2θ +1). Book:- Differential Equations, by Dennis G Zill, page ,number 17.
23 Polynomials Problems : Solving for Roots, Asymptotes, Word Problems, Finding Equations from Roots, Synthetic Division and Function Composition
1. The figure shows the graphs of f(x) = X 3 and g(x) =AX 3.What can you conclude about the value of a? 2. If f(x)= x(x+3)(x-1), use interval notation to give all values of x where f(x)>0. 3. If f(x) =x(x-1)(x-4)2 , use interval notation to give all values of x where f(x)>0. 4. Find the quotient and remainder of f(x) =
I had to prove 4 theorems two of them dealt with Abelian elements, automorphism of R2 under compontentwise addition. I want to keep my original work in tack as possble BUT I would like the follwing corrections made based on the following comments. THESE ARE THE ISSUES THAT NEED TO BE ADDRESSED The paper needs to provide
A geologist you spoke with is concerned about the rate of land erosion around the base of a dam. Another geologist is studying the magma activity within the earth in an area of New Zealand known for its volcanic activity. One of the shortcuts they apply when doing calculations in the field is to use synthetic division. After t
(See attached file for full problem description) The problem is solved by integration and evaluation between the limits and algebraic manipulation
Discuss an element of drinking water where you see a public health gap or need that should be addressed. You may bring up a specific case relevant to your community if you have one, or bring up a global issue.
List 4 problems dealt with by cryptography & give real world examples of each. 2 paragraphs please.
(See attached file for full problem description) --- Suppose that a(x) and m(x) are relatively prime polynomials in F[x]. Bézout's Theorem guarantees the existence of polynomials u(x) and v(x) in F[x] such that... --- (See attached file for full problem description)
6301 is prime. If x, y, and z are integers that are not divisible by 6301, which of the following is equal to x^6299.y^12600.z^18903 mod 6301 ? (a) xyz (b) yz2/x2 (c) z3/x (d) 1/(x2 y2) (e) none of the above
Which of the following is true. a) 16 is a non-trivial square root of 1 modulo 51; hence 51 is composite b) 7 is a non-trivial square root of 1 modulo 47; hence 47 is composite c) 8 is a non-trivial square root of 1 modulo 55; hence 55 is composite d) all of the above e) None of the above
Q.1 For a number x, with 1< x < p, the number x^n mod p can be computed with at most 2log2 n modulo p multiplications. Asymptotic notation questions Q.2 2^(2n) = O(2^n) Q.3 log*n = O(log*(log n)) Q.4 The sqrt n th Fibonacci number can be computed and written in O(log n) time Please see the attac
1. Find the prime factorization of 54. ____a. 220.127.116.11 _x__b. 18.104.22.168 ____c. 2.2.17 ____d. 22.214.171.124 2. Determine which of the following is divisible by 3. ____a. 3106 ____b. 2251 _x__c. 1239 ____d. 1172 3. Determine which of the following is divisible by 8. __x_a. 1336 ____b. 1473 ____c. 1534 ____d.
Does a prime number multiplied by a prime number ever result in a prime - Why? Does a nonprime multiplied by a nonprime ever result in a prime - why? Is it possible for an extremely large prime to be expressed as a large integer raised to a very large power? Explain. Are there infinitely many natural numbers that are not pri
1) Let e = ... be an RSA enciphering exponent. Prove that, for any... Please see attached.
The Mobius Inversion Formula 1) Prove that ∑ μ(d) φ(d) = Π (2 - p) d/n p/n Primitive roots modulo p 2) Find all primitive roots modulo 5, modulo 9, modulo 11, modulo 13 and modulo 15. Prime Numbers 3) The Fermat numbers are numbers of the form 2^(2^n) + 1 = φn . Prove that if n < m, then φn| φm - 2 4) Prove that if n ≠ m, then gcd (φn, φm) = 1 5) Use the above exercise to give a proof that there exist infinitely many primes.
Theory of Numbers Mobius Theorem