Problem 3: pe 197 241 (random PRIME number in the interval [150,200]) (random PRIME number in the interval [200,250]) 9= a) Using the Quadratic Reciprocity Law, determine if (p/q)-(q/p) b) Show how to use Theorem 9.6 to find (2/p) and (2/q). c) Show how to use Theorem 9.10 to find (3/p) and (3/q). d) Find (p/q). Show any work that you did.

Q: 6. (a). [3-2 စာ ၅၊ = Let A 1-1-2 = 0-2 Compute A-1 ***** (b) Use part a) to fin all solutions to the…

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Q: Compute √27 using once False Position method with x₁ = 1 and x = 2. A 1,69 B 1,84 1,93 1,78

A: We have to compute 275 using the method of False position once where xl=1 and xu=2

Q: (Proof by cases: (p₁ V P2 V (Pn →q)) Prove or disprove. V Pn) → q = (P₁ → q)^(p2 →q)^^...^ "The 4th…

A: Let x be any integer.  We need to prov        x4 does not leave remainder 2 when divided by 3.…

Q: Q2 Consider nonnegative integer solutions of the equation…

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Q: Show that =- 5)" /31 + 6. 1 = 2 ) /7! + () /9! – ... %3D | -- IN

A: We know that, from the Taylor's formula for power series expansion of sinx is given as…

Q: e O Di) what's A B c) A) B) another (-1+73)/10 (1 - 1) /2 (1-7) / 8 (-1 +7i)/4 f(x) has a f(x) f(x)…

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Q: 4. The conventional algorithm for evaluating a polynomial anx" + an-1x¹ +... + a1x + ao at x = c can…

A: Algorithm Polynomial (c, ao, a1,...,an: real numbers) power = 1; y = a0 ; for i = 1 to n power =…

Q: 5. if we have two polynomials pl=3x5 + 8x* – 2x2 + 4x + 1 p2= 2x6 + 3x* – x² + 4x Find:- Your answer…

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Q: a) For an odd prime p, prove that the quadratic residues of p are congruent mod p to the integers…

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Q: f in a AP the sum of m tern=ms is equal to n and the sum of n terms is equal to n then prove that…

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Q: b) iv)

A: Part 2: Explanation:Step 1: Identify the contour C:The contour C is defined as the set of complex…

Q: Prove or disprove 4|[(2²n-1 + 4)"]⁰

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Q: solve the quadratic congruence 7x^2 - 8x +4 = 0 (mod 17)

A: The given problem is to solve the given quadratic congruence equation 7x2-8x+4 = 0(mod 17)

Q: can you pls show the full solution on how you come up with that answer,

A: I will show the full solution for the first question so that you can get the other in the similar…

Q: - Use the division algorithm to find the quotient q and the remainder r when dividing f(x)=x³+x² + 4…

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Q: (a) If a, b,c € Z+ and a +b=c then (c,[a, b)) = (a, b).

A: As you asked multiple questions , so I solved only the first one.

Q: Exercise 2.8. Let a, b be real numbers and let a ^= (₁ 1) A and B -(1) What is AB ? Compute A² and…

A: We use method of induction to prove A^m .

Q: 7. Theorem 94 I (9x-25)

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Q: 6 -1 Let A =| 0 -2 and B . Compute (AB)". Show your work. 4 3

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Q: Solve the polynomial congruence x^3 - 3x^2 + 27 = 0 (mod 225). Please be detailed! I’m really…

A: Solution are fully explained in below steps Explanation:

Q: If in a AP the sum of m tern=ms is equal to n and the sum of n terms is equal to n ,then prove that…

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Q: Use the properties of the Legendre Symbol and the quadratic reciprocity theorem to calculate (88…

A: From properties of Legendre's symbol we have, ,  this is  Law of Quadratic Reciprocity.

Q: Use Hensel’s Lemma and Chinese Remainder Theorem to find all solutions to x^2 + 3x + 17 ≡0 (mod 300)

A: Introduction: Hensel’s Lemma is a powerful tool in number theory that allows us to lift solutions of…

Q: Prove this statement: we have numbers {a1, a2, a3 .,a2n} which are even and positive, but 0 < {a1,…

A: As, we know that, A.M.≥G.M. ---(1) A.M. of numbers, a1,a2,a3...a2n=a1+a2+a3+a4...+a2nn G.M. of…

Q: 2a)ii

A: Step 1: Step 2:

Q: + a3 + a5) – (@2 + đ4)I 4 [(a1 + a3 + as) – (a2 + a4)] [(B1 + B3 + B5) (a2 + a4) + A (B2 + Ba) (a1 +…

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Q: n —(2) - (-) (1)¹(1)(). (n-1)

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Q: 10. By Binomial Theorem (2a – b)* =16a* – 32a’b+24a*b? – 8ab³ +b* | a. TRUE. b. FALSE.

A: We know the binomial therom expansion

Q: 1. The conventional algorithm for evaluating a polynomial a„x“ + an-1x" at x = c can be expressed in…

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Q: Show that (6+c) ba са (c+a) cb =2abc(a+b+c) ab 3 (a+b) ас bc

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Q: EC»(a-p)- = Ip + (1- p)" = 1" = 1.

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