Compute (3714 - 39) mod 9 without a calculator.

Q: Find the answer of -16 mod 5

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Q: Find an integer x satisfying the equation: 4x21 = 2(mod 5) or show that no such integer exists.

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Q: Find the solution to 34x = 77(mod 89) that is positive and less than 89.

A: given that                                          34x≡77 (mod 89) we have to find positive…

Q: find x, where x= 9753 (mod 120) and -120<x<0

A: Ans: -87

Q: Find the smallest integer a > 1 such that a –1 = 2a (mod 11

A: To find:

Q: Find 12 ^– 1(mod 17), the inverse of 12 modulo 17

A: Find an inverse of 12 modulo 17 as follows.

Q: Find the value of 3443 mod 23 4 16 O 3

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Q: Find d the inverse of 43 mod 6602

A: we use Euclidean algorithm to find the inverse of 43 mod 660.

Q: x is congruent to 43 mod 12. Then x is None of the option 91 75 89

A: Answer is 91.

Q: Compute 2021^2021(mod 1000). The answer is 421. Show the work.

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

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Q: Find all solutions in {0, 1,2, ..., 12} to x26 + 15x13 = 12 mod 13.

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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: The inverse of 7 modulo 26 is 15

A: Given a statement

Q: Find the four solutions of x* = 1 (mod 13).

A: Since you have asked multiple questions we will solve the first question for you .To get any…

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: Prove that 2^10 + 5^12 is a composite number.

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Q: Determine which of the following statements are true: a. 54=72(mod16)

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Q: 16.5. Compute 2 (mod 9991) by successive squaring and use your answer to say whether you believe…

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Q: 3x = 11 (mod 20)

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Q: 2) Find 281171 + 171281 (mod 12)

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

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Q: 23219 Compute 11 mod 3. Show your work and justify each step.

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Q: x is congruent to 43 mod 12. Then x is None of the option 89 91 75

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Q: Consider the congruence 9x   21 (mod 33). (a) Does 9 -1(mod 33) exist? Explain why or why not.

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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: Find a number a such that 70a = 1 mod 17.

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Q: Is 103= 58 mod 5 true or false?

A: Note: a mod b is the remainder from the division of a by b. Given: 103 = 58 mod 5.

Q: What is 62019 =   mod 5

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Q: (d) For all integers a and b, if ab = 7 (mod 12), then either a = 1 (mod 12) or a = 7 (mod 12).

A: (d) For all integers a and b, if ab=7 mod 12, then either a =1 mod 12 or a =7 mod 12

Q: Find all solutions of x = 10 (mod 133).

A: A congruence of the form, f(x)≡0(modm), where f(x)=anxn+an-1xn-1+...+a1x+a0, ai=0,1,2,...,n is…

Q: 10. Use Euler's Theorem to show that 5P(16), '=1 (mod 16). Show your work or explain your reasoning…

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Q: Find (177 mod 31 + 270 mod 31) mod 31. Show your wor-

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Q: Prove that no integer congruent to 3 modulo 4 can be written as the sum of two squares.

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Q: Find all solutions of 3* = 17 (mod 224)

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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: Find all solutions in {0,1,...,43} to 6x=10 mod 44

A: In general,  ax ≡ b (mod m) has solution if gcd(a,m) divides b    If gcd(a,m) = 1 then solution is…

Q: If a = 2846463 mod 59, then a =? A

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Q: Does

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Q: Find 5483. mod 13.

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Q: 2222 (mod 13) is equal to 12 (mod 13) 2 (mod 13) None of the mentioned 6 (mod 13) 1 (mod 13)

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Q: Solve for a a ≡ 13 mod 5353

A: To solve  a ≡ 13 mod 5353

Q: Find a number a between 0 and 86 such that 71122 = a (mod 87).

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Q: (b) Solve the set of congruences 2x =1 (mod 5) x=3 (mod 4)

A: Note:- We’ll answer the first question according our protocol. Please submit a new question…

Q: Find the solution to 2x = 7(mod 17) that is positive and less than 17.

A: We find solution of given congruence relation

Q: Find all the integers that satisfy 140x = 133 (mod 301).

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Q: 4. Find 2001 (mod 205). (Enter the least non-negative integer

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Q: What is the smallest positive integer x in the equarion: 1=3x+2(mod 7)?

A: We have to solve the equation 1 = 3x + 2 (mod 7)⇒1 - 2 - 3x = 0 (mod 7)⇒-1 - 3x = 0 (mod 7)⇒3x = - 1…

Q: Number theory

A: