Which of the following linear congruence has 2 incongruent solutions? (a) 3x = 9 (mod21) (b) 14x = 12 (mod20) (c) 8x = 21 (mod16) (d) 3x = 7 (mod8)

Q: Solve the linear congruence 7x = 13 (mod 19).

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Q: What sequence of pseudorandom numbers is generated using the linear congruential generator xn+1 =…

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Q: The equation 20x=30 (mod 70) has: 10 non-congruent solutions modulo 70 None of these no solution…

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Q: Solve for x: 7x = 3 mod 11

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Q: x^2 ≡ 1 (mod 105)

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

Q: Find all solutions to the system of congruences: x ≡ 7 mod 12 x ≡ 37 mod 45 2x ≡ 134 mod 150

A: The given problem is to find the all solutions which satisfies the given system of linear…

Q: Find all whole number solutions of the congruence equation.  2x+1≡ 5 mod 4 3x+1≡ 4 mod 9

A: The given problem is to find the whole number solutions for given system of linear congruence…

Q: 2X=3 mod 5 Show your work

A: the given congruence equation is 2x≡3mod 5 the general congruence equation is ax≡bmod c…

Q: Solve the linear congruence 8x = 407 (mod 1405)

A: We need to solve the linear congruence Let us first find the inverse of 8 mod 1405

Q: For this question, explain the reason if no solution exists. Give a complete list of solutions if…

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Q: then x* 1 is odd." Give a proof by contradicton to show "1fx s even integer,

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Q: Solve the linear congruence 10x ≡ 15 (mod 45).

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Q: Take the last four digits ABCD of your student identification number, and let AB and CD be the…

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Q: 7) Solve the system of linear congruences below: x = 2 (mod 7) x = 10 (mod 15) x = 9 (mod 26)

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Q: The linear congruence 7x = 3(mod16) is solvable of solution: O None of the choices

A: The given problem is to solve the linear congreunce equation, we have to use congruence properties…

Q: 3. Solve the system of congruences x = 1(mod 5) x 2(mod 6) r= 3(mod 7)

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Q: 5. Using congruence theory (not brute force), find all solutions to the following linear congruence:…

A: Note:- A two variable linear congruence ax+by≡m    mod (n) has solution if and only if  gcd ( a, b,…

Q: . (a) How many quadratic residues are in the residue set Z19? (b) Determine if 4 and 9 are quadratic…

A: Introduction: Quadratic residue is a part of congruent modulo theory. It is a non-linear congruence.…

Q: Suppose that p is a prime with p = 5 mod 8 . Show that the congruence px2 + 6y = 1 mod 3p has no…

A: Consider the given information.

Q: Determine the system of linear congruences which yeild all the square roots of 31 modulo 33.

A: Please find the answer in next step

Q: The system 2x + 3y = 4 (mod 4) 3x + 4y = 5 (mod 4) has no solution modulo 4. Select one: True False

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

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Q: Solve the linear congruence x3 – 7x² – 48x + 18 = 0 ( mod 54).

A: Please note that, As you have asked Answer number 10 , so I answered only Number (10).

Q: The 4th term of an ap is zero. Prove that 25th term of the AP is three times its 11th term

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Q: Use Hensel's Lemma to find a solution to the following congruence: a +3 x + 3 = 0 mod 54.

A: Let f(x) be a polynomial , p is a prime number . If x=a is a solution of congruence equation…

Q: Find all the non-congruent solutions to  4x ≡ 6(mod 21)  express solutions using the stand…

A: Introduction: A linear congruence is generalized as ax≡bmod n. The greatest common divisor of a and…

Q: 2. Solve the system of congruence 3x +7y = 10 ( mod 16) (5x + 2y = 9(mod 16) .

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Q: Solve the congruence: 341x ≡ 2941 (mod 9).

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Q: 2X+3=1 mod 5 Show your work

A: We have solve given problem:

Q: Solve the system of congruence x ≡ 3(mod6) and x ≡ 4(mod7) using the method of back substitution.

A: System of congruence equations

Q: Find the first few terms of the sequence of pseudorandom numbers generated using the linear…

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Q: 5) Solve the system of linear congruences below: x ≡ 6 (mod 9) x ≡ 10 (mod 13) x ≡ 18 (mod 29)

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Q: The equation 21x=49 (mod 70) has: * O None of these O no solution modulo 70 6 non-congruent…

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Q: 2. Solve the system of congruence 3x +7y = 10 ( mod 16) 5x+2y 9( mod 16).

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Q: Find the first few terms of the sequence of pseudorandom numbers generated using the linear…

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Q: Show that th equation x" + y² = z" (mod 5) has nonzero solutions in Zz if and only if n is odd.

A: Given: xn+y2n≡zn(mod 5)

Q: he solution of the linear congruence 103x = 444 (mod 999) is ) 111 ) 222 2 333 ) 444

A: We have to find x such that  103x = 444(mod 999)

Q: Find the first few terms of the sequence of pseudorandom numbers generated using the linear…

A: Given below an step by step solution

Q: What sequence of pseudorandom numbers is generated using the linear congruential generator xn+1…

A: Determine the sequence of pseudorandom numbers generated using the linear congruential generator…

Q: Solve the congruence 9x   21 (mod 33).

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Q: Find all the whole number solutions of the congruence equation. 3x 8 ≡ mod 11 3x + 12 ≡ 7 mod 10

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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

A: Since you have posted a multiple question ,I will solve the first question(i.e.Q3)  for you. To get…

Q: Find all solutions of quadratic congruence x^2+85x+2=0(mod401)

A: We follow the method of completing the squares of the equation x^2+85x+2. Note that 85 is odd so we…

Q: Solve the system of congruences 2x + 6y = 3 (mod 15) 3x + 7y = 6 (mod 15)

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Q: Number of solutions for the congruence equation x^2 + 2x + 1 = 0(mod 52) is

A: The given congruence equation is x2+2x+1 = 0(mod 52)

Q: the number of incongruent solution of the congruence 8x = 10(mod6) is: 2) 8. 4

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Q: ulus) 1) Solve the following congruences system. 5x +4 = 12 (Mod 7) 14x - 3 = 19 (Mod 5) 2) Prove…

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Q: Find all solutions, to the system of congruences x ≡ 8 (mod 15), x ≡ 5 (mod 6) and x ≡ 3 (mod 10) if…

A: We will find out the required solution for given system of congruences.

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.