X=4(mod nod 13) X2-7(mod 15)

Q: Find all solutions to 17r = 14 (mod 21).

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

A: The given question is solved below.

Q: Solve a congruence equation and give all the solutions: 3(x – 2) + 4x = 5x +8 (mod 31)

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Q: Find a primitive root of 29 Solve x6 = 4 (mod 29)

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Q: Find all solutions of the congruence x2 ≡ 29 (mod 35).

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Q: How many square roots of 3 (mod 1001) are there? (Hint: 1001 = 7 * 11 * 13)

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Q: For which integers c, 0<c < 30, does the congruence 12x == c (mod 30) have solutions? When there are…

A: Given congruence is 12x≡c(mod 30). We know that ax ≡b(mod m) have solutions when gcd(a,m) divides b.…

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

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Q: Verify 2 is a primitive root mod 13, and then answer the following: Find a solution to x5 = 11 mod…

A: If p is prime, then b is a primitive root for p if the powers of b include all of the residue…

Q: The least positive integer solution for the congruence 2x = 14 (mod 18) is Answer:

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Q: Find all integer solutions to the equation 23. + 6x2 + x + 6 =1 mod 74. Explain your method and cite…

A: en x3+6x2+x+6 = 1 mod 71

Q: 10. (8 points) Solve 3x 2, (mod 7) or show that no solution exists.

A: Solution: The objective is to find the solutions of 3x≡2 (mod 7)

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: Find all solutions to x^2=6 mod 143, note that 143=11*13 (I solved x^2=133 mod 143, but i'm not sure…

A: It is required to find all the solutions of x2=6mod143 Given that 143=11×13 Where 11 and 13 are…

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

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 5x = 7 (mod 32)

A: To solve the following problem

Q: The liñear congruence 9x = 19 (mod27) has 3 incongruent solutions. :Select one True False

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Q: Solve each equation for x.  5x ≡ 2, (mod 7), x, (mod 7) 7x + 1 ≡ 4, (mod 11), x, (mod 11)

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Q: perform the indicated operations: 8+11(mod 12)

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

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Q: 5. Solve the congruence 11x = 15 (mod 20). (Write all solutions)

A: we have to solve                                      11x≡15(mod 20) greatest common factor of 11…

Q: The equation 21x=49 (mod 70) has: 6 non-congruent solutions modulo 70 7 non-congruent solutions…

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Q: #5. Suppose that a = 2 (mod 113), and b = 5 (mod 113) What is (a b + 56b + 155) mod 113?

A: given a≡2(mod113),b=5(mod113)a3≡23(mod113)a3b≡235(mod113)56b≡280(mod113)56b≡54(mod113)155≡15mod113)

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

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Q: Does x2 + 5x congruent to 12 (mod 31) have a solution? (Hint: complete the square)

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Q: Write the set of solutions of x=5 (mod 24) x= 17 (mod 18), if any as the solutions to a single…

A: We have a set of congruence as x ≡ 5 (mod 24)x ≡ 17 (mod 18) From the first equation we can write…

Q: the number of incongruent solution of the congruence 8x = 10(mod6) is: 1. 4 2) 8)

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Q: b) Determine whether or not x? = 85 (mod 97) has a solution.

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Q: The value of 52003 mod 7 is? (3 4 8

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Q: 6), then the congruence has a unique solution modulo p. 11. Show that the congruence x³ = 3 (mod 19)…

A: 11. To prove that the congruence x3≡3 mod 19 has no solutions, whereas x2≡11(mod 19) has three…

Q: 24. Given the linear congruence (16x is congruent to 72 mod 24.) How many possible incongruent…

A: 24. To find the number of incongruent solutions of16x≡72mod 24

Q: 1. x=2 mod 3 2. 9x = 21 mod 30

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Q: The equation 82x = 12 (mod 13) has O 1 incongruent solution modulo 12 O 4 incongruent solutions…

A: First Option Is Correct Answer.

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

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

A: The given congruence equation is                                             3x+12≡7 mod 10

Q: The equation 82x = 12 (mod 13) has O 1 incongruent solution modulo 12 O 4 incongruent solutions…

A: The given equation is 82x = 12(mod 13)

Q: 3

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Q: True/False: If 10x = 20 (mod 8) holds, then x = 2 (mod 8) must be true.

A: True.

Q: mod 32, given Xo=1 Please answer w

A: The congruential generator is given as:Xi+1 = 11Xi mod 32, where we are given X0 = 1. We see that,…

Q: The linear congruences a = 3 (mod 9), x = 9 (mod 24) has simultaneous unique solution modulo .…

A: The given system of linear congruence is: x≡3(mod 9)x≡9(mod 24)

Q: solve by means of a derivation, the congrucnce equation; 10x= 4 (mod 2a) Express ansurer in form X=…

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Q: Exercise 5 Find all integer solutions to the following equations. (1) a? =5 (mod 312). (2) a? – 4x +…

A: 1  The equation can be written as: x2=5x=±5x=5   or  x=-5. Hence, there will exist two real value…

Q: Solve the congruence 2² +1 =0 mod 133.

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Q: Which is the solution of 71x congruent to 5 mod 142. 38 57 85 None of the above

A: To determine which of the given is the solution of 71x≡5mod142.

Q: Number theory

A:

Q: Does

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Q: The linear congruences x = 3 (mod 6), x = 9 (mod 15) has simultaneous unique solution modulo. .....…

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Q: Does ?2 ≡ 23 (mod 79) have any solutions. Justify your answer using the Legendre symbol.

A: Note that the congruence X^2= 23 (mod 79) will have solution if and only if 23 is a quadratic…

Q: 4. Solve the congruence 34.x = 77 (mod 89).

A: in first process firstly we need to find the inverse to solve this type of question

Q: 2x = 1(mod 5) 31( mod 7) 5x 9(mod l)

A: