Exercise 3. 3x +1= 2 (mod 9) a has no solution modulo 9 b. has six non-congruent solutions modulo 9 c. has a unique solution modulo 9 which is 2(mod 9) d. has only three non-congruent solutions modulo 9 which are 2(mod 9), 5(mod 9). and 7 (mod 9)

Q: What is the number of solutions to the congruence in Z125? x³ + x² + 3 = 0 (mod 125)

A: As per the question we have to solve the following polynomial congruence equation : x3 + x2 + 3 ≡ 0…

Q: If x = y (mod n) and u = v (mod n) then which of the following is false. (a) x+ u = y +v (mod n) (b)…

A: Given that x≡ymod n and u≡v mod n. By definition, x≡ymod n implies x-y is divisible by n. Then let,…

Q: For each statement, indicate whether it is true or false. Then prove or disprove it. (a) For all SC…

A: (a) FALSE.  Consider S ⊆ℤ, defined by  S = { 2+8k | k ∈ℤ } U { 2+12r | r∈ℤ }.  Then the given…

Q: Prove that if ax = b (modn) then () x = () (mod ()) where d = gcd(a, n). Apply this result to 5x =…

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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: Solve the system 3x + 2y = 5 2x + 7y= 9 mod 17 mod 17

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Q: x = 2 (mod 5) 2r = 22 (mod 8) 3x = 12 (mod 21) (i) How many solutions does it have lying between 0…

A: i)Given thatNotice first that the moduli are pairwise relatively prime, Therefore, we can use the…

Q: 1. Solve the Congruence x^5 ≡ 2 (mod 7)   2. Solve the congruence x^7 ≡ 10 (mod 23)   Show work…

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Q: 4. 8x = 12 (mod 20).

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

Q: The least positive solution modulo 330 for the system x = 2(mod 5) x = 1(mod 6) T = 3(mod 11) is x =

A: Want  to find: The least positive solution modulo 330 for the systemx≡2 mod 5x≡1 mod 6x≡3mod 11we…

Q: Solve : ex+ay =4 (mod 13) E 2 2 (mod 13) Using elimination

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Q: (3) If today is Thursday what day of the week will it be 31 days from today? (4) If it is currently…

A:

Q: 2. Encrypt the message STOP POLLUTION by translat- ing the letters into numbers, applying the given…

A: let's encrypt the message "STOP POLLUTION" using the given encryption functions one by one.For the…

Q: 5. Explain why the congruence r = 2 (mod 4) has no solutions in Z.

A: We have to show that the congruence x2≡2(mod 4) has no solution in ℤ

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: Exercise 34 Solve the following equations: 1. 5x +3 = 7 (mod 11). 2. 4x + 5 = 11 (mod 13). 3. 9x – 4…

A: As per our guidelines we are supposed to answer?️ only 3 subpart from multiple questions. Kindly…

Q: In Exercises 15 to 18, find possible whole number solutions of the congruence equation. 15. x = 7…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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

A:

Q: 7. Solve the congi 8. Solve the system of congruences x = 3(mod 7) x = 5(mod 8) lid?

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Q: Which of the following are true modulo 12? (1) Does 5z = 6 mod 12 have a solution? How many? (2)…

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Q: Exercise 34 Solve the following equations: 1. 5x + 3 = 7 (mod 11). 2. 4x + 5 = 11 (mod 13). 3. 9x –…

A: Here we will find out the required value

Q: 1 Solve the following system of congruences X= 2 (mod 3) x = 3 (mod 5) X= 2 (mod 7)

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Q: Solve 107p = 136 (mod 1001).

A: Introduction: “Since you have posted multiple questions, we will provide the solution only to the…

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: The equation 15x=30 (mod 50) has: 5 non-congruent solutions modulo 50 6 non-congruent solutions…

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Q: Does 5x = 6 mod 12 have a solution? How many?

A: As per our guidelines we are supposed to answer only One question  if there are multiple questions…

Q: -) Find the solutions, if any, of each congruence. 21x 10 (mod 35) 9x = 15 (mod 21).

A: We know that, ax≡b mod n has solution if and only if gcd(a,n) divides b.

Q: which one will give a solution of [6,13] a)4x is identical to 3 mod 7 b)9x is identical to 11 mod…

A: which one will give a solution of [6,13]

Q: Suppose that a and b are integers, a = 4 (mod 13), and b = 9 (mod 13). Find the integer c with 0 < c…

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Q: What is the number of solutions to the congruence in Z125? x³ + x² + 3 = 0 (mod 125)

A: In the question we are given the following polynomial congruence equation : x3 + x2 + 3 ≡ 0 (mod…

Q: Consider the congruence a² + x + 1 = 0 mod 21. Solutions to the congruence above must also be…

A: The given congruence equation is .We will solve this congruence relation using the Chinese remainder…

Q: Why does the linear congruence 25x ≡ 30 (mod 75) have no solutions?

A: To show that the linear congruence 25x≡30mod 75 have no solutions.

Q: Test 1

A: Step 1: For x2  ≡ −1 (mod 39+), check if -1 is a quadratic residue modulo 39 Step 2: Calculate the…

Q: Solve the system 3x + 4y = 5 7x + 5y = 6 mod 17 mod 17

A:

Q: Which are true for modulo 12? 1.) Does 5x ≡ 6 mod 12 have a solution? How many? 2.) Does 4x ≡ 6 mod…

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Q: Solve 55x ≡ 2(mod243) by inverse method.

A: Given 55x≡2mod 243. Solve this congruence using the inevrse method.

Q: Solve for x given i) x^5=21 (mod 43) ii) x^7=2 (mod 35)

A: To find out the value of x.