One of the following is a solution of 81x = 54 (mod 108) 43 47 45 42 has no solution

Q: Consider the equation where x1,x2,...,x9 € N. How many solutions are there if: a) b) c) Xi 9 for all…

A: As per the question we are given a linear equation : x1 + x2 + ... + x9 = 73 And we have to find the…

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

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: Q2: Solve the following (if possible): 1. = 5x + 11 mod 37 3

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

Q: Suppose b is any integer. If b mod 12 = 5, what is 6b mod 12? In other words, if division of b by 12…

A: Given b is an integer such that b mod12=5 To find the value of  6b mod12

Q: 2. Solve the Root Mod x = 3 (mod 11) xE [5]10 OxE [7]i0 none of these xE [7]1 Oxe[5]1

A: Use Farmet's theorem

Q: Perform the following calculations. a. (14 + 30) mod 19 b. (14-30) mod 19 C. (3*13) mod 19

A: To perform the given calculations we shall use the following rules…

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

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

A:

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

A:

Q: 16. Which of the following congruencies has NO solution? . A. 24x = 18(mod 39) B. 5x = 4(mod 10) C.…

A:

Q: 6. Solve 11x = 4 (mod 21) (a) 8. (b) 4 (c) 11 (d) has no solution

A: given 11x≡4 mod 21 since gcd11,21=1 thus, we can write 11x=4+21y for some y

Q: 1. Solve each of the following. 14x = 1 (mod 45) 24x = 35 (mod 59) а. b. 62x = 1 (mod 99) С. d.

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Q: x is congruent to 31 mod 6. Then x is 40 54 55 None of the option

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Q: The integer solution of the 2x³ + 7x – 4 = 0(mod 5), then а) х—4(тod 25) b) x = 1(mod 5) c) x =…

A: Congruence

Q: The value of 52003 mod 7 is? 80 3) 4

A:

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

A:

Q: The solution for xr° =10(mod11) is a) 5 b) 6 c) No solution d) 4 Answer A D Submit

A:

Q: One of the following is a solution of 306x = 90 (mod 360) 107 has no solution 105 106 108

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Q: i need to find the value of m 12 = (m*28)mod 113

A: Solution is given by using Diophantine equation and extended Euclidean algorithm as follows

Q: The solution for x =10(mod11) is: а) 5 b) 6 c) No solution d) 4

A: The objective is to find the solution for x8=10mod 11

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

A:

Q: Does x2 + 5x congruent to 12 (mod 31) have a solution? (Hint: complete the square)

A:

Q: Given 3 * 4.52 = x(mod 53), Here x is equal

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

Q: Determine whether the following systems have unique solution, infinitely many solutions or no…

A:

Q: Find the value of x if any. Show your complete solution. 1.   (13 + x) = 3 mod 16 x = 2.   (3x +…

A:

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: 4. 2x = 3 (mod 5)

A: A congruence ax≡b(mod n) has a solution only if  gcd(a,n) divides b. Also to solve a congruence…

Q: Suppose b is any integer. If b mod 12 = 7, what is 5b mod 12? In other words, if division of b by 12…

A:

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: Solve the following congruence equations. 1. x=2 mod 3 2. 9x = 21 mod 30 3. 18x = 30 mod 42

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Find the integer a such that a ≡ 71( mod 47) and -46  ≤ a ≤ 0  I need a better understanding of how…

A:

Q: 1. x=2 mod 3 2. 9x = 21 mod 30

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Q: b. 3x = 0 (mod 21)

A:

Q: Find an integer x that satisfies the equation. 5* = 4(mod 11) 17x?=10(mod 29) i. %3D ii.

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Q: or what values of k, x=4 will be a solution for 3x²+4x = k mod31?

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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: The number of mutually incongruent solution(s) of 306x = 90 (mod 360) 20 30 18 O 6 0

A:

Q: 4. Solve the following: 34x 60 (mod98) 5. Detemine all the possible positive m values greater than 1…

A:

Q: "Given: x = -30 (mod 12) Which of the following integers are valid solutions for x 18- O 30 20 36-

A: Solution:- -30mod(12) To obtain -30mod12 conduct these three steps:

Q: 2. Let A = {n? + n € Z :n € Z} and B = {r € Z : r³ – 32³ + 2x = 0 mod 5}. Prove or disprove: A B.…

A: That's easy, just needs a little congruence. Have a great day!!!

Q: The number of incongruent solutions of 105x = 45(mod60) is: 6 12 None of the choices 15

A:

Q: 3. Find a solution to the following systems, if possible. a) X = 2 (mod 21) and X = 3 (mod 91) b) 2X…

A: Find the 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: Does ?2 ≡ 23 (mod 79) have any solutions. Justify your answer using the Legendre symbol.

A: Note that the congruence X^2= 23 (mod 79) will have solution if and only if 23 is a quadratic…

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

A: ANSWER IS 12 NON  CONGRUENT SOLUTIONS MODULO 48

Q: (a) Find an integer r E {0,..., 196} which solves the equation 167 = 7 (mod 197).

A: Given equation is x157≡7mod197. We have to find that an integer x∈0,....,196 which solves the…

Q: 10. Solve the following modular congruences or show that there is no solution. (^) 10r =1 (mod 31)…

A: We will find out the required value.

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.