The equation 82x = 12 (mod 13) has O 1 incongruent solution modulo 12 O 4 incongruent solutions modulo 12 O 6 incongruent solutions modulo 12 None of the choices

Q: Find all solutions to 17r = 14 (mod 21).

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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: The equation 82r = 12 (mod 13) has O 1 incongruent solution modulo 12 O 4 incongruent solutions…

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Q: What are the FOUR values of x that will satisfy: x ≡ 4 mod 5 & x ≡ 3 mod 7 please show your…

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Q: Either solve the congruence, giving the solution as a least residue, or show that it has no…

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Q: For which integers c, 0<c < 30, does the congruence 12x == c (mod 30) have solutions? When there are…

A: Given congruence is 12x≡c(mod 30). We know that ax ≡b(mod m) have solutions when gcd(a,m) divides b.…

Q: The number of mutually incongruent solution(s) of 306x = 90 (mod 360) 18 2

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Q: (i)Find the inverse of 5(mod9)     (  ii)Hence or otherwise solve simaltaneous equation…

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Q: (1) Consider the equation 2.x +1 = 0 mod n. For which n are there no solutions? one solution?…

A: Congruence

Q: For this question, explain the reason if no solution exists. Give a complete list of solutions if…

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Q: How would I solve for n and m (without a calculator)? Please explain. 5" = 3( mod 97) 5m = 7( mod…

A: to find the value of m , n when 5n≡3 mod 975m≡7 mod 97 (i) we can write 5n≡3 mod 97 as   5n=97s+3…

Q: The least positive integer solution for the congruence 2x = 14 (mod 18) is Answer:

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Q: 1. Solve each of the folling. а. с. d. 115x = 2 (mod 288) 2. Explain why 12x = 1 (mod 75) has no…

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Q: Consider 64z 16 mod 196. The number of solutions mod 196 is Oa None Ob 3 Oe 1

A: We find the number of solutions incongruent mod 196

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: Find all solutions to x^2=6 mod 143, note that 143=11*13 (I solved x^2=133 mod 143, but i'm not sure…

A: It is required to find all the solutions of x2=6mod143 Given that 143=11×13 Where 11 and 13 are…

Q: The equation 6** = 9 (mod 13) has 1 incongruent solution modulo 12 3 incongruent solutions modulo 12…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: (a) Solve for x if 25x = 15(mod 29).

A: Linear congruence

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

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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…

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Q: Solve each equation for x.  5x ≡ 2, (mod 7), x, (mod 7) 7x + 1 ≡ 4, (mod 11), x, (mod 11)

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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: Solve the equation 5x = 13 (mod 18)

A: Given: To solve: the equation 5x4≡13mod 18Formula: a≡bmod cis equivalent to saying by Euclid's…

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

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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: The equation 21x=49 (mod 70) has: * O None of these O no solution modulo 70 6 non-congruent…

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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: 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: Use your work from problem 2 and the method used in the example at the end of Lecture 16 to solve…

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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: The equation 82x = 12 (mod 13) has O 1 incongruent solution modulo 12 O 4 incongruent solutions…

A: First Option Is Correct Answer.

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: olve the congruence8x= 16 (mod 424).  If none exists, explain why.  If there are one or…

A: The given equation is: 8x≡16mod 424

Q: 3

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Q: A sequence of pseudorandom numbers is generated as follows Xo = 4 x₁ = ( 6x₁-1 + 5 ) mod 13 if i > 0…

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Q: In the congruence equation 3x + 12 = mod 10, which of the following is FALSE O a. 5, 15, 25, 35,..…

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Q: solve by means of a derivation, the congrucnce equation; 10x= 4 (mod 2a) Express ansurer in form X=…

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Q: 3x is congruent to 2 mod 13

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Q: the number of incongruent solution of the congruence 8x = 10(mod6) is: 2) 8. 4

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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: The equation 30x≡24 (mod 48) has: * 24 non-congruent solutions modulo 48 no solution modulo 48 None…

A: ax≡b (mod m) has solutions if and only if gcd(a,m) divides b. Moreover the number of non-congruent…

Q: The equation 21x = 49 (mod 77) has: O no solution modulo 77 only 7 non-congruent solutions modulo 77…

A: Solution

Q: The equation 12x=24 (mod 48) has: O 24 non-congruent solutions modulo 48 6 non-congruent solutions…

A: To find- The number of solutions for the given equation.

Q: Either solve the congruence, giving the solution as a least residue, or show that it has no…

A: We will check whether the given system of congruence has solution or not.

Q: c. Find all non-congruent solutions to x? = 1 (mod 15) d. Find all non-congruent solutions to x2 = 4…

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Q: 4. Solve the congruence 34.x = 77 (mod 89).

A: in first process firstly we need to find the inverse to solve this type of question

Q: The number of mutually incongruent solution(s) of 307x = 83 (mod 360)

A: BY THE DEFINITION OF Modulus congruence Modulus congruence means that both numbers, 16 and 21 for…

Q: Determine four values of x that will satisfy: x ≡ 4 mod 5 & x ≡ 3 mod 7 please show your solution

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Q: Which of the following is a solution of congruence equation, 4x –7 =3 (mod 10)?

A: We will find out the required solution.

Q: Solve the Diophantine equation 7x + 5y = 43 by  rst solving the congruence 7x = 43 (mod 5), which is…

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