Find the primitive roots (mod 17).

Q: Find the answer of -16 mod 5

A:

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: {X = I (mod 3) 2X= 2 (mod 5)

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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: just give the handwritten solution. Solve the congruence: 7x^5 congruent to 6(mod 17)

A: The solution is given below

Q: Solve the congruency by finding the inverse: 7x = 9(mod 43)

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Q: Find the smallest positive integer x that solves the congruence: 7x≡5 (mod52)

A: 7x≡5 (mod52)---(1)

Q: x is congruent to 43 mod 12. Then x is

A: x is congruent to 43 mod 12 implies x congruent 7 (mod 12). So, solution in the least residue system…

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: 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: Where would 129 be on a mod 13 clock (which goes from 0 to 12)? What is the remainder…

A: Where  would  129  be  on  a  mod  13  clock  (which  goes  from 0 to 12)? What is the remainder…

Q: Find all the primitive roots modulo 125.

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Q: Find the modulus and argument of the com

A: Given,          7-xi5+3i2 and  x = 2.

Q: 1. Give the ten 10th roots of unity. Write them in the form e. Among these 1Oth roots, which are the…

A: According to Bartleby's guidelines, we are allowed to answer only one question at a time. So here is…

Q: Calculate the inverse of 15 mod 26 (i.e., solve 15 * x ≡ 1  (mod 26))

A:

Q: Find the solutions of the congruence 15x2 + 19x ≡ 5 (mod 16).

A: Congruence modulo relation on integers:Let a,b∈Z and let m be a fixed positive integer. Then we say…

Q: X = 17 (mod 21) X= - ) 8 Cmod 25

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

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Q: Find the integer that satisfies: 30x4 ≡ 12 (mod 67)

A: Given the expression is, 30x4≡12mod 67

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: Find all integer values of x for which 3x = 4 (mod 8).

A: given congruence equation 3x≡4(mod 8)

Q: Number theory

A:

Q: X=1 (mod 81) and X = 7 (mod 12), as the solutions to a single congruence.

A: It is given that X=1mod81 and X=7(mod12) Here a1=1,a2=7,n1=81,n2=12 Therefore:…

Q: Using Fermat's theorem, find 3201 mod 11.

A: Euler's Theorem states that for any natural  number n, we  have  aϕ(n)≡1(mod n) where ϕ(n) denotes…

Q: The order of 5 mod 17 is

A: “Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: The order of 5 mod 17 is *

A: Since ϕ(17) = 16 Therefore order can be the divisor of 16 So the order can be 1,2,4,8 or 16

Q: The number of incongruent primitive roots modulo a prime p is: a) Ø(p) b) Фф — 1) с) р—1 O a O b

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Q: Find all solutions for 10x = 14 mod 1008

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Q: Find all solutions of the congruence x2 ≡ 16 (mod 105).

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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: b. 3x = 0 (mod 21)

A:

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: Find the mod of (2-4i)^1/2

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Q: Number theory

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Q: Find, with proof, all primitive roots mod 27.

A: To find all primitive roots mod 27,

Q: #1. Find all five 5" root of Z = 32cis40° 5th

A: Given z= 32 cis 40° rewrite it as z= 32cos 40+isin 40 if z= rcos θ+isin θ then n distinct complex…

Q: Does

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Q: Show that 2 is a primitive root of 19.

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Q: There are no primitive roots modulo n = 128. O False True

A: Theorem: There are no primitive roots modulo 2n for n>2.

Q: Use the repeated squaring method to calculate the following: 16^10 (mod 230)

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Q: The equation 12x=24 (mod 48) has:

A: ANSWER IS 12 NON  CONGRUENT SOLUTIONS MODULO 48

Q: Solve for a a ≡ 13 mod 5353

A: To solve  a ≡ 13 mod 5353

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

A:

Q: Find the smallest positive integer xx that solves the congruence: 11x≡5(mod57)

A: