VI. Determine four values of x that will satisfy the following. 16. x = 4 mod 5 & x = 3 mod 7 17. x = 9 mod 11 & x = 3 mod 10 18. x = 2 mod 4 & x = 3 mod 6 19. x = 1 mod 3 & x = 5 mod 8

Q: A. 5x = -127 mod 15.

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Find all solutions for x, up to congruence. x ≡ 1 mod 4 and x ≡ 7 mod 13.

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Q: QUESTION 1 Find an integer x between 220 and 260 that satisfies x = 39^123 (mod 41). Your answer…

A: We need to find integer x between 220 and 260 that satisfies x = 39123 mod 41 Clearly , 39 and 41…

Q: 1. Solve each of the folling. а. с. d. 115x = 2 (mod 288) 2. Explain why 12x = 1 (mod 75) has no…

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Q: 1. Solve each of the following. 14x = 1 (mod 45) 24x = 35 (mod 59) а. b. 62x = 1 (mod 99) С. d.

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Q: Consider 64z 16 mod 196. The number of solutions mod 196 is Oa None Ob 3 Oe 1

A: We find the number of solutions incongruent mod 196

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

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Q: 2.23 Find all four solutions to the equation x²10 (mod 35).

A: The given equation is: x2-1≡0 mod 35 We have to find all four solutions to the given equation.

Q: Ans Encryt the message GO" by translating the letter, into number, applying the given encrytion…

A: We will use the basic knowledge of number theory and cryptography to answer this question completely…

Q: Q7. Solve the following set of simultaneous congruences. 4x = 1(mod 5) 6x = 5(mod 11) 2x = 5(mod 13)

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Q: 1. A+B (mod 173) 2. C-D (mod 432) 3. 23 x E (mod F) 4. G+5 (mod 7) АВМ 1А A B C E F G Hannah 7550…

A:

Q: Find the solutions of a3 – 24.x2 + 54 = 0( mod 25).

A: want to find solution of x3-24x2+54≡0(mod 25)note that1 a≡b(mod m) f and only if m|a-b(i.e a-b=mk…

Q: Find all solutions for x, up to congruence. (b) x ≡ 11 mod 142 and x ≡ 25 mod 86.

A: Given: (b) x≡11 mod 142 and x≡25 mod 86 To find: All solutions for x, up to convergence.

Q: Find the multiplicative inverse mod 26 for α = 19. Show all steps.

A: In the given problem we have to find the multiplicative inverse mod 26 for α = 19. Show all steps.

Q: (3) Solve for x (give your answer as an integer between 0 and 7: 14 · 51 ≡ x(mod7)

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Q: 2x = 4 (mod 8) a. has no solution b. has infinite solutions c. has a unique solution modulo 8 which…

A: Here 2x≡4 (mod 8). Hence 2x=4+8k, for some integer k. Dividing by 2, x=2+4k, for some integer k.…

Q: C. Determine whether each linear congruence is solvable. 4.276y=3476 (mod 1276) 5. x = 3 (mod 9) 6.…

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Q: For each of the following equations determine if they have a solution. If yes, find the solutions,…

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Q: D. Determine the number of incongruent solutions of each linear congruence. 1. 22x = 18 (mod 75)…

A: Given linear congruence is  1. 22x≡18mod 752.   2z≡119mod 983.   9x≡95mod 36

Q: 1. Using set notation, determine each solution set. . х %3D 1 тоd4&x 3D 1 тоd 5

A: Here questions 1,2,3 are unrelated since anyone can be solve without any help of another. So by…

Q: Solve each equation for x. (If there is no solution, enter NO SOLUTION.) (a)     x + 8 ≡ 1, (mod 9)…

A: We solve each equation for x.

Q: Use calculus to sketch the graph of the given function. (a) f(x) = 3x* – 4xr

A: Consider the given function, fx=3x4-4x3 Here we need to sketch the graph of the given function using…

Q: For each pair of integers m and d, calculate m mod d. Show your work! a. m = 43 and d = 9 b. m 50…

A: If m and d be two integers . Then m mod d means that the remainder when m is divided by d .

Q: 2) Solve for x (give your answer as an integer between 0 and 9): 51 + 27 ≡ x(mod10)

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Q: y²=x³-5x+3 (mod5). solve for all x and y, when x is at least 0, and y is at most 4

A: Using congruence and modular arithmetic we solve the given equation. We substitute the value of x…

Q: 3. Let a be a primitive 10th root of unity. Which of the following is false? A. a5 = 1 B. a³ = a¹3…

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Q: One of the following is a solution of 81x = 54 (mod 108) 43 47 45 42 has no solution

A: We are given the Equation :

Q: VI. Determine four values of x that will satisfy the following. 16. x = 4 mod 5 & x = 3 mod 7

A:

Q: Q7. Solve the following set of simultaneous congruences. 6x = 1(mod 5) 5x = 3(mod 11) 2x = 5(mod 13)

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Q: b) Find an integer x such that 37x = 1 (mod 101).

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Q: 12. Solve for x. 14 18 &r

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Q: 5. Which of the following are inverses of each other? (a)3, 7 w.r.t. mod 20 (b)2, 5 w.r.t. mod 9…

A: Explanation of the answer is as follows

Q: or what values of k, x=4 will be a solution for 3x²+4x = k mod31?

A:

Q: Which of the following is not a possible value for y ≡≡ 17 mod 8 in the equation ? Group of answer…

A: Consider the given equation.

Q: Find all solutions to x ≡ 1 mod 2, x ≡ 2 mod 3, and x ≡ 3 mod 4

A: We need to find all solutions to x ≡ 1 (mod 2)             x ≡ 2 (mod 3), and x ≡ 3 (mod 4 ) of this…

Q: 9. a. Solve xQ + Q – 4 = 3Q + 5 (mod 2Q), where Q = 2 b. Find the quotient and remainder when Q is…

A: 9. a) Given congruence is xQ+Q-4≡3Q+5mod 2Q where Q=2 Using the value Q=2 in the given congruence…