(32³ mod 13)² mod 11

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: 2x = 1(mod 5) I (mod 4x = 1(mod 7)

A: We need to solve the system of linear congruences given by 2x≡1(mod 5)4x≡1(mod 7)

Q: 4444 is divided by a 1.19) find the remainder when 4444 * 2?=-1 (mod a).

A: 1.19 We have 4444  ≡  7 (mod 9). So, 44444444 ≡ 7 4444 (mod 9) Now,       73 ≡1 (mod 9) Or,…

Q: b=3(mod19)

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Q: Suppose that a and b are integers such that a = 45 (mod 71) and b = 53 (mod 71). Find an integer c…

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Q: Find all values of x (using congruent notation) for 35x ≅ 3 (mod 89)

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Q: 2. Determine x >0 for each case: 5903 = x (mod 60), 17342 =r (mod 5).

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Q: Find 1112 mod 13.

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Q: (b) Compute 9-¹ (mod 19) by listing the multiples. Show your work.

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Q: (a) Prove the following: i. 11 + (6 x 4") - 22n = 6 mod 7, 1 is divisible by 131, ii. 8260 iii.…

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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: 10 Solve 3Y=2 (mod 7) 8 Salutions exist or show that

A: We have to solve given problem:

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

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

A: True.

Q: true or false? explain this: 2 mod 5 ≡ 7 mod 5

A: a mod n  ≡ b mod n if n divides (a-b).

Q: 4. Determines the result of the following operations: a. (27 – 3) (mod 5) b. (56 – 14) (mod 7) c.…

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