Suppose n = pq with p and q distinct odd primes. (a) Suppose that gcd(a, pq) = 1. Prove that if the equation x^2 ≡ a (mod n) has any solutions, then it has four solutions. (b) Suppose that you had a machine that could find all four solutions for some given a. How could you use this machine to factor n?

Q: You find yourself on a plane in space, whose coordinates are given by  -x - y + z = -1. At a point A…

A:

Q: x1 x2 x 3 Xx4 +s x1 +x2 x1 x2 +x3 X3 +x4 +x4 = = 1 2 -3

A:

Q: Consider the discrete-time dynamical system xt+1 = 5xt(1-xt). If xt = 4/5, xt +1 = _____ Is x1 = 4/5…

A: Let xt+1=f(xt) be a difference equation , then x=x* is said to be equilibrium if xt+1∗=xt∗⟹…

Q: Evaluate the integral of the function f(x, y) over the region R that is bounded by the x-axis, the…

A: To set up the integral of the function  over the region R bounded by the x-axis, the line  and the…

Q: Solve the linear programming problem using the simplex method. 5x + y ≤ 80 9x + 2y ≤ 100 x≥0,y 20…

A:

Q: Solve the system 21 X2 = I3 X4 4x₁5x₂ + 3x3 +3x4 +₂ +3x3 +2x4 3x₁4x2 +6x3 +5x4 -2x₁ +2x₂ +63 +4x4…

A:

Q: Consider the following integral. Sketch its region of integration in the xy-plane. 0 If (a) Which…

A:

Q: 17. The following function describes the motion of an arrow shot upwards. The height h in meters…

A: 17. The following function describes the motion of an arrow shot upwards.The height h is in meters…

Q: An electrical repairer charges 339 of the cost of a new motor for a rewinding job. IL the motor…

A: Given that, an electrical repairer charges  of the cost of a new motor for a rewinding job.The new…

Q: 7. Approximate the square pulse distribution below on the interval x € [−1,1] using Legendre…

A: The given function  is defined on the interval  and defined as follows..We need to approximate…

Q: f(t) = sinhtcost

A:

Q: Then where a11 where C11 = a12 = C12 = a21 = C21 = a22 C22= A 1 = (§ 8), B= ( − 4 ³ ) ,0 = (1 ²).…

A:

Q: How many free variables does each augmented matrix have? a. Choose b. Choose c. Choose d. Choose ✓…

A:

Q: For the following system to be consistent, 5x-5y+5z = 6 9x+1y+kz=-9 -2x-3y+7z = 5 we must have, k‡

A:

Q: Q6. SR2, 800 is needed for a purchase. The buyer has SR2, 500 and will invest the money at 9% annual…

A:

Q: Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux.…

A:

Q: Given the following vector x, find a non-zero square matrix A such that Ax=0: You can resize a…

A:

Q: Write the linear programming problem as a maximization problem with all inequalities (except x 20, y…

A:

Q: In Exercises 26-37, give an algebraic specification fo the null space and the range of the given…

A: Given algebraic specification for the null space and the range of the given matrix A.34.

Q: Find the particular solution corresponding to the tableau. x=y=₁z=₁u=₁v== X y z 1 -4 0 1 0 7 0 1 0 u…

A: from given table we have seen that basic variable in the current table are So from table we have…

Q: A cylindrical tank having a radius of 0.5 meters and a height of 2 meters is half-full of kerosene,…

A: Given that a cylindrical tank has a radius 0.5 meters and height 2 meters. The cylinder is half-full…

Q: Find the greatest common divisor of 32 * 73 * 11 and 34 * 72 *

A:

Q: Solve each of the following simultaneous systems of congruences (or explain why no solution exists).…

A:

Q: In each of Problems 1 through 26: (a) Find the general solution in terms of real functions. (b) From…

A: Given Information:The differential equation is .Objective:a) Find the general solution.b) Analyze…

Q: Prove the following statement using its contrapositive. Let m and n be two integers. If m² + n² is…

A: I have solved the question. Please go through that.

Q: Given the differential equation: dy dx + (1 + y²) = 0 y(0) = 0 a. Show that the differential…

A:

Q: Prove that the dual of l' is isometric to 10⁰.

A: Accounting to the given data, prove the given statement:

Q: 1.a) Graph f(x) = ¼ for 2 ≤ x ≤ 6 distribution is this? b) What kind of

A: for

Q: Write down the equation of motion for the point particle of mass m moving in the Kepler potential…

A:

Q: 1 121 In Exercises 18-21, interpret the subset W of R³ geo- metrically by sketching a graph for W 2…

A: The given subset W of R3 is written as follows..We need to interpret the subset .

Q: I1 X2 I3 I4 Solve the system +8 +t 4x₁15x₂+2x3 +4x4 -I1 +₂ +3x3 +3x4 3x₁4x2 +5x3 +74 2x₁2x₂ - 6x3…

A:

Q: Use graphical methods to solve this linear programming problem. Maximize subject to: OA. The maximum…

A:

Q: (b). Given y=8x²°, y=0, x = 1₁ first we find the area! 8x3 A = SS dA I fox³ dydx [ [y] 8x³² dx = 8…

A: In this question, we will check the given answer is correct or not.

Q: For a = 2695, b = 1820, use the prime factorizations to find lcm(a, b) and gcd(a, b). Verify that ab…

A: Given thata = 2695  and   b = 1820We have to find lcm(a, b) and gcd(a, b) by using prime…

Q: Let T: R³ R³ be a linear transformation with standard matrix A. Let P be a parallelepiped in R³. If…

A: Given Information:It is given that  is a linear transformation with the standard matrix . is the…

Q: A transformation f: R³ → R² is defined by f (x1, x2, X3) = (x₁ − x₂ + 2x3, 2x1 − X2 −X3). i. Show…

A:

Q: 1. Draw a two-dimensional figure that could be rotated using a vertical axis of rotation to give the…

A:

Q: Exercise 1. A student is asked to prove If m is even and n is odd, then m² + n² is odd. 2 The…

A: Let us answer above questions

Q: Below are the tables representing six different functions. Identify which func tions are aven, odd,…

A: A function is an even function if f(-x) =f(x), and it is an odd function if f(-x)=-f(x). We need to…

Q: 3. Let f(x) = x² - 6. With po = Use the Secant method. a. b. C. 3 and pi Use the method of False…

A:

Q: 1. Consider the following optimization problem: minimize 2x1 + x2 + x3 subject to x2-x3 = 0 5x1 +…

A: (a) No, the given problem is not a linear programming problem. The objective function 2x1​+x22​+x3​…

Q: Determine whether the following system has no solution, an infinite number of solutions or a unique…

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Solve the linear ODE by integrating factor method: (x^2)y’ + xy = 1

A:

Q: -2 1 -¤-B and B = 4 2 A = E₁ = Given the following descriptions, determine the following elementary…

A:

Q: Match each function (a, b, c, d) with its derivative and explain how you knew. Not all derivatives…

A: Match each function (a, b, c, d) with its derivative and explain how we knew.Not all derivatives…

Q: Determine whether the given set S is a subspace of the vector space V. A. V=P3, and S is the subset…

A: We need to determine that given subsets are subspaces of corresponding vector spaces.We know that a…

Q: The image shows a dilation of an equilateral triangle by scale factors of 1, 2, 3, and 4. At each…

A: Given Information:An image is provided as a dilation of an equilateral triangle by scale factors .At…

Q: Find the length of the arc of the curve 27y² 27y² = 4(x - 2)³ from (2,0) to (11,6√3)

A:

Q: Explain how each of the following features relates to a function's derivatives and curve sketching.…

A:

Q: List all the isomorphisms between the two graphs given in Figure 12.23. Explain why there are no…

A: