EULER’S EXTENSION TO FERMAT’S THEOREM A.Find the remainder when 5^85 is divided by 28 B.Find the remainder when 2^400 is divided by 33

Q: Raj purchases a new home for $120,000. The value of the home increases by 11% every 3 years.…

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Q: (2) (C) Show that C = 6 ||abER} a, commutative ring with unity even if M₂ (R) is not. Finally, show…

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Q: 3. Find the points of intersection of the parabola ²-4x+y=0 and the line-2x+y=-3

A: Let the co-ordinate of the intersection point be (x, y).  Then (x, y) lies both on the parabola and…

Q: 8. Use Sagemath (or any other method) to calculate the first 30 terms of each of the Taylor series…

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Q: II. For each of the functions, indicate whether they are continuous at the indicated point. If the…

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Q: в dt dy dt = 2x+y x+2y 1 2t e

A: Given : dxdt=2x+y-e2tdydt=x+2y  x0=1 , y0=-1 To Find : Solution of Initial value problem.

Q: (a) Consider y=-3y + 2y+2x+3 y(0)=2. y(1)=1 0≤x≤l By using N=2 i.e. h=, write the system of…

A: Please find attachment

Q: 2. Let vectors a = (3, 1, 2), b = (0, 2, 1), and c = (1, 1, -1) be given. Find (2a + 3b). c. • Find…

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Q: (i) State the cancellative law in a group G. (ii) Give the definition of the group GL2(R). iii) Give…

A: A group G, * is a set G together with binary operation * satisfies the following properties. Closure…

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Q: where ao, a1, , an are fixed constants. Consider the nth order linear differential equation ...3…

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Q: 3. Write the following statements in symbolic language and prove each of them: (a) for all r ER,…

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Q: Fermat's little theorems A.Find the remainder when 3^58 is divided by 19 B.Find the remainder when…

A: We will find the remainder using Fermat's little theorem of the following : 1.   Remainder when  358…

Q: 18. Determine whether the given propositional forms are logically equivalent. a. p (qr) and (p q) ^…

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Q: Answer these questions for the partial order represented by the given Hasse diagram. a Yes or No b…

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Q: X y 41.4 -345.4 24.2 -501.1 33.6 255.3 35.1 645.1 48.3 1159.1 37.5 411.5 40.3 -446.1 44.1 513 41.1…

A: Correlation Coefficient: X Y X - X (X - X)2 Y-Y (Y-Y)2 (X-X)(Y-Y) 41.4 -345.4 -6.293 39.60185…

Q: Write z₁ and z2 in polar form. Z1 = Z2 = Z1 Find the product Z₁Z2 and the quotients and Z2 Z1 Z1Z2 =…

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Q: 5. For what value of the constant c is the function f continuous on (-0, 0) < f(x) = {cx²-20 [cx²-2c…

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Q: A rocket is being launched. After a while, it rises at a constant velocity of 5 miles per second. An…

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Q: thinking of a whole number. If I divide it by 13, then multiply the answer by 12, then subtract 20,…

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Q: QUESTION 5 If the determinant of the 3x3 matrix 3 a -1 2 b 10 1 12 5 is 7, then what is the…

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Q: Prove that C is not the splitting field of any polynomial in Q[x].

A: In this question, we have to show that ℂ is not the splitting field of any polynomial in ℚx. We know…

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A: Please find the attached image.

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Q: Let G be a finite group generated by a and b. Let s1, s2, . . . , sn be thearcs of a Hamiltonian…

A: Given that 'G' be a finite group generated by a and b. Let s1, s2, . . ., sn  be the arcs of a…

Q: If f, g, and h are f A(x) = (xf)' (x²f)" A'(x) = f f' (x³f")" differentiable 8 (xg)' (x²g)"…

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Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 1. Determine the values of "a" and "b" in such a way that the…

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Q: Prove whether this statement is true or false. For all sets A, B, and C: (see image)

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Q: 12 1 3 4 Let = b₁ = LMTA | 2 | 3 | D | - | - - - - - - - - |-| b₂ = b3 = and = 7 16 -3 19 18 a. Find…

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Q: Evaluate the following e-5 using two approaches X³ 31 +-- ---- and e-* ex=1-X+²+ =1/4 +*+ ** ex =…

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Q: Let a be a repeated root of a quadratic equation f(x) = 0 and A(x), B(x), C(x) be polynomials of…

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Q: A federal report indicated that 18% of children under age 6 live in poverty in Iowa, an increase…

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Q: QUESTION 10 Let's try to the Gram-Schmidt process of orthogonalization with the matrix 0.223 0.668…

A: Given matrix 0.2230.6680.710-0.1250.7410.6600.795-0.2340.560 Let  r1=0.223, 0.668, 0.710r2=-0.125,…

Q: Solve the equation. 2x + 5 x+13_ x+8 + 9 9 6 = What is the solution set? Select the correct choice…

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Q: If n EN, then 1-3+2-4+3-5+4-6+...+ n(n+2) = n(n+1)(2n+7) 6

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Q: y X y 1 2 831 1073 y = 4 3 1317 1715 Use exponential regression to find an exponential equation that…

A: Sol:- Exponential Regression:- The curve to be fitted is y=aebxtaking logarithm on both sides, we…

Q: 2. a) Polynomial equations with certain characteristics have no real solutions (x-intercepts). Give…

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Q: 1. Evaluate the following integral: [ 8(x+b)dx where a, b are constants. a 2h

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Q: A as the product of two determinants, show that A = 0. Hence, show that if ax² + 2hxy + by² + 2gx +…

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Q: 2. Verify wh

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Q: Identify the correct steps involved in showing that every totally ordered set is a lattice. (Check…

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Q: 74 +4 Z Show that the Complexfunction f(z) = Z(Z-21) havearemovable discontinuity at z=2₁

A: The given problem is to show that the given complex function f(z) have a removable discontinuity at…

Q: The size of product BA is?

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Q: Find the dimension of the subspace spanned by the given vectors. 1 0 4 - 2 1 -7 - 11 4 - 40 8 - 3 29…

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Q: Consider point P(x, y) in first quadrant. Its reflection abou x-axis is Q(x₁, y₁). So, x₁ = x and y₁…

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Q: The function f(x) = 2* is transformed to become g(x) = 2x What is the effect on f(x)? of(x) is…

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Q: Consider the differential equation x²dx-ydy=0 with the initial condition y(0) = 2. Approximate the…

A: dydx=x2y, y0=2, h=0.2 yn+1=yn+16k1+4k2+k3k1=hfxn,ynk2=hfxn+h2,yn+k12k3=hfxn+h,yn+2k2-k1

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Q: Find general solutions of the systems in Problem Attached.

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Q: A certain electronics manufacturer found that the marginal cost CC to produce x DVD/Blu- ray players…

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