Q3/ Use Chinese theorem to solve the following congruence: X=2 mod 3 X=1 mod 5 X 2 mod 4

Q: What is the number of solutions to the congruence in Z125? x³ + x² + 3 = 0 (mod 125)

A: As per the question we have to solve the following polynomial congruence equation : x3 + x2 + 3 ≡ 0…

Q: Prove that x113+x-1≡0(mod 113) has no solutions in x.

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Q: ​Q3// Use Chinese theorem to solve the following congruence: X ≡ 2 mod 3 X ≡ 1 mod 5 X ≡ 2 mod 4

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Q: (10) Find all solutions of the congruence 2 = 22 (mod 53). C

A: We shall be using primitive roots to solve this congruence.

Q: x^2 ≡ 1 (mod 105)

A: Given: x2≡1(mod 105) To Solve: The given congruence  x2≡1(mod 105)

Q: Q16

A:

Q: Find all solutions of the congruence 8x ≡ 4 (mod 12)

A: Step 1: Divide by the greatest common divisor (GCD)The GCD of 8 and 12 is 4. We can divide both…

Q: solve the congruence 2²-7x+6=0(mod3³.7³)

A: Given congruence: Objective: Solve the congruence equation and find the solutions for  modulo .

Q: Solve the con Congruence 1x²=6 (mod17)

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Q: ions of the congruence 15x^2 + 19

A: Given:- 15x2+19x≡5 mod 55

Q: Solve the linear congruence 2370x ≡ 69 (mod 2517) or say why no solutions exist

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Q: he linear congruence 132x ≡ 76 (mod 100) has a solution. Select one: True False

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Q: Solve the system 3x + 2y = 5 2x + 7y= 9 mod 17 mod 17

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Q: Suppose x^3 = 1 (mod 41). Show that x = 1 (mod 41).

A: Given that: x3≡1mod 41. We have to show that x≡1mod 41.

Q: Find the common solutions to the congruences 2x 3x 4x 1 (mod 5) 9 (mod 6) 1 (mod 7).

A: Given : 2x≡1 (mod 5)3x≡9 (mod 6)4x≡1 (mod 7) To find : The common solutions to the congruences. For…

Q: x43 = 47 (mod 713)

A: Step:-1 By Chinese remainder Theorem (CRT),  x43 ≡ 47 mod 713 if and only if x43 ≡47 mod 23 ⇒x43 ≡1…

Q: Solve the congruence 11x = 45 (mod 97) where x is an integer in the interval [0,97).

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Q: 1. Solve the Congruence x^5 ≡ 2 (mod 7)   2. Solve the congruence x^7 ≡ 10 (mod 23)   Show work…

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Q: Solve the givnen congruence x2 ≡ 9 (mod 600).

A: The given problem is to solve the given congruence equation. x2=9 (mod 600).

Q: -3x = 4{mod8}

A: 3x = 4 (mod 8)  We have to find all integral value of x.

Q: 5. Explain why the congruence r = 2 (mod 4) has no solutions in Z.

A: We have to show that the congruence x2≡2(mod 4) has no solution in ℤ

Q: Solve the congruence3x−7 = 2 (mod 16). Your solution should be positive and reduced modulo16.

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Q: for a fixed n>1 Show that all the solvable congruences x2 ≡ a ( mod n ) have the same number of…

A: To Proof: For a fixed n>1 , all the solvable congruences x2 ≡ a ( mod n ) have the same number of…

Q: Find the solutions of the congruence 15x2 + 19x ≡ 5 (mod 65)

A: The given equation is: 15x2+19x≡5(mod 65)

Q: Show that there are no integers a, b such that a² + 2ab+26² = 100000000003. Hint. Use mod 4…

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Q: . Find all the solutions of 3x² + 2x + 1 8 (mod 63).

A: Given a quadratic congruence in the form:Ax2+Bx+C=0(mod n)multiply the above equation by…

Q: X = 17 (mod 21) X= - ) 8 Cmod 25

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Q: Simplify (15-54)(mod 4). (15-54)(mod 4) =(mod 4)

A: Simplify          (15 - 54)(mod 4)

Q: 1 Solve the following system of congruences X= 2 (mod 3) x = 3 (mod 5) X= 2 (mod 7)

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Q: Demonstrate that the equation x10 + y10 - z10 = 5 has no integer solution. (work with modulo 11)

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Q: Solve the quadratic congruence x² = 35 (mod 817).

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Q: Find all solutions of the systems of congruences: = 12 (mod 25) 22 (mod 35).

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Q: 1. Prove that any quasigroup satisfying one of the identities {(ry)x satisfy the other. = y, z(yr)…

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Q: 2) Solve the following linear congruences: 14x = 91 (mod 189) 24x = 56 (mod 88)

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Q: If possible, find a complete set of mutually incongruent solutions of each of the following…

A: The given congruences, a) 9x≡12mod 15. b) 81x≡57mod 117. We have to find the solution to the…

Q: Use Chinese theorem to find all positive integers that makes this congruence true:        x = 2 mod…

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Q: Use the index system modulo 19 to find all solutions of x³ = 11 (mod 19) and 5ª = 4 (mod 19)

A: In the theory of congruence, Fermat's little theorem is very significant. It says that for any prime…

Q: find the congruence for the following congruence equations: (1) 18x=3 (mod47)

A: First and second question are independent .So According to guideline I am solving first one.The…

Q: What is the number of solutions to the congruence in Z125? x³ + x² + 3 = 0 (mod 125)

A: In the question we are given the following polynomial congruence equation : x3 + x2 + 3 ≡ 0 (mod…

Q: congruences using the modular inverses found in question 11. 4 (mod 141) 34 (mod 89) Solve the…

A:

Q: Solve the linear congruence 7а + 3у %3D 10 (тod16).

A: Consider the linear congruence 7x + 3y ≡ 10 mod 16.Since gcd (7, 3) = 1 we know at least one…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.