11.5. For each part, find an x that solves the given simultaneous congruences. (a) x = 3 (mod 7) and x = 5 (mod 9) (b) x = 3 (mod 37) and x = 1 (mod 87) (c) x = 5 (mod 7) and x = 2 (mod 12) and x = 8 (mod 13)

Q: 5. 2x 15 (mod 17) 6. 4x 6 (mod 17)

A: According to our guidelines we can do at most three subpart of a question at a time. So please post…

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

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Q: 1. Find all solutions (a) 2x + 3 = 7 (b) 2x + 3 = 7 to the following congruences.. (mod 9) (mod 20)

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

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Q: Find all solutions of the system. 3x = 1 (mod 5) 2x = 3 (mod 7) 5x=11 (mod 3)

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Q: 36. Find all solutions to each of the following linear equations: a. 3x= 4 (mod 5) b. 4x = 4 (mod 6)…

A: a)  In modular arithmetic, you can find the solution by multiplying both sides of the congruence by…

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: Can you please show me step by step for this math that makes me undertandable. Q: Determine which…

A: (a) For the congruence 4x ≡ 5 (mod 6), we need to find a solution for x such that when 4x is…

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

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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: 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: 1. Solve each of the linear congruence equations or verify that it has no solution. (i). 3r = 4(mod…

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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: If possible, solve the following linear congruences. (a) 42x = 1014 (mod 91) (b) 42x = 1015 (mod 91)

A: If possible, we have to solve the following linear congruences.

Q: The remainder when aa is divided by 77 is 22 and the remainder when bb is divided by 77 is 55. (So a…

A: Given:          a≡2 mod(7)  and b≡5 mod(7)

Q: How do I use the Chinese Remainder Thm to solve this system of congrunces below? x ≡ 1 (mod 3) x ≡ 4…

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

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Q: By using the CRT, solve the system 4x ≡ 2 (mod 6 ), 3x ≡ 5 (mod 7 ), 2x ≡ 4 (mod 11 ).

A: Given, 4x≡2 mod 63x≡5 mod 72x≡4 mod 11 It can be written as,  x≡12 mod 6x≡53 mod 7x≡42 mod 11 Here,…

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

A: