b) Determine whether or not x? = 85 (mod 97) has a solution.

Q: Solve the linear congruence 7x = 13 (mod 19).

A:

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)

A:

Q: Solve a congruence equation and give all the solutions: 3(x – 2) + 4x = 5x +8 (mod 31)

A:

Q: If mx = 1 (mod n) has a solution, then nx = 1 (mod m) has no a solution. Select one: True False

A: We know the definition of Congruence ,  Suppose m be a positive integer , we say that integers a and…

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

A:

Q: 1. How many solutions( mod 419) does x = 186 mod 419 have? (Show your work!) 2. How many solutions (…

A: Given: x2≡186 mod 101 We need to solve x2≡186 mod 101 and how many solution exists.

Q: Find all integer solutions to the equation 23. + 6x2 + x + 6 =1 mod 74. Explain your method and cite…

A: en x3+6x2+x+6 = 1 mod 71

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

A:

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: Solve the givnen congruence x2 ≡ 9 (mod 600).

A: The given problem is to solve the given congruence equation. x2=9 (mod 600).

Q: Find all the whole number solutions of the congruence equation.x x 5 mod 9

A: The objective is to find all the whole number solutions of the congruence equation.x x = 5 mod 9

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

A:

Q: Does x2 +3x+7=0 mod 31 have solutions? IF

A: This follows in the same way as we study quadratic equations. Here we use facts about quadratic…

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

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Q: perform the indicated operations: 8+11(mod 12)

A:

Q: Solve the congruence: 341x + 19 = 291 (mod 9).

A:

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

A:

Q: What is 2 ^32 mod (5)?

A: mod is the function whose output is always positive. mod is represented by .

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

A:

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: Solve x2+3x+2 is congruent to 0 (mod 55)

A: 55=5×11 and gcd(5,11)=1, hence they are co-prime.The given system of equation x2+3x+2≡0mod 55 is…

Q: Number theory

A:

Q: Explain why the following linear congruence has no solutions:   5x ≡ 16 (mod 45).

A: Explain why the following linear congruence has no solutions: 5x ≡ 16 (mod 45).

Q: Use Hensel Lifting (twice) to find a solution to x² = 7 (mod 374).

A: According to the given information, it is required to use Hensel lifting method to find the…

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

A:

Q: Find the solutions of the congruence 15z + 19x = 5 (mod 11)

A: This question is related to Number Theory

Q: The value of 52003 mod 7 is? (3 4 8

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: Explain why the congruence r2 = 2 (mod 4) has no solutions in Z

A: Result: Square of all integers modulo 4 is either 0 or 1.…

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: 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: 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 solutions to the congruence13x−3 = 4 (mod 26). If none exists, explain why.Your…

A:

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

A: The given equation is 82x = 12(mod 13)

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

A:

Q: To solve the equation 13x 6x + 14 = 0 (mod 19) is equivalent to solve

A:

Q: Does

A:

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: 2x = 1(mod 5) 31( mod 7) 5x 9(mod l)

A:

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: Number theory

A:

Q: What are the FOUR values of x that will satisfy: x=2 mod 4 & x=3 mod 6 please show your…

A: Given: x≡2 mod 4  & x≡3 mod 6   x≡a(mod m1)x≡b(mod m2) has a solution if and only if…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.