Solve the Diophantine equation 7x + 5y = 43 by  rst solving the congruence 7x = 43 (mod 5), which is equivalent to 2x   3 (mod 5).

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

A:

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

A: The given question is solved below.

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

A:

Q: (3). (a). Find all solutions to the congruence 6x = 9 (mod 45)

A: To Determine :-  All solutions to the congruence : 6x ≡ 9   mod 45 .

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

A:

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

A: The solution is given below

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

A:

Q: Solve the linear congruence 2370x ≡ 69 (mod 2517) or say why no solutions exist

A:

Q: Solve the linear congruence 8x = 407 (mod 1405)

A: We need to solve the linear congruence Let us first find the inverse of 8 mod 1405

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

A:

Q: 1. Solve the following linear congruence using a systematic method: 167x = 241 (mod 199) Present…

A:

Q: Solve the congruence17x−3 = 4 (mod 26).

A:

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: Find the four solutions of x* = 1 (mod 13).

A: Since you have asked multiple questions we will solve the first question for you .To get any…

Q: а). Solve the linear congruence of 231x = 147 mod 598 .

A:

Q: Solve the linear congruence 10x ≡ 15 (mod 45).

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

A:

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

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: a) Find all solutions to the congruence 10r = 5 mod 15

A: Given,

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: 8. Solve the linear congruence, 30k + 14 = 5(mod 11).

A:

Q: Solve the linear congruence x3 – 7x² – 48x + 18 = 0 ( mod 54).

A: Please note that, As you have asked Answer number 10 , so I answered only Number (10).

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

A:

Q: he linear congruence 132x = 76 (mod 100) has a solution. elect one: D True D False

A: I will use the property of linear congruence relation.

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

A:

Q: the number of incongruent solution of the congruence 8x = 10(mod6) is: 1. 4 2) 8)

A:

Q: Solve the congruence: 6x ≡ 4 (mod10)

A: The congruence could be written as,

Q: The quadratic congruence x^2+4x+1=0 mod 7 is solvable True False

A: Since not a particular question asked as per guidelines ,solution to only first question is given…

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

A:

Q: For the congruence 17x ≡ 9 (mod 276), write down an equivalent system of congruences. Hence solve…

A: We have to Write down an equivalent system of congruences and Hence solve the congruence 17x ≡ 9…

Q: 2) Solve the following linear congruences: 14x = 91 (mod 189) 24x = 56 (mod 88)

A:

Q: Question 2 Solve the linear congruence 19x =7 (mod 90127)

A: We have to Solve given linear congruence by following way.

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

A:

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

A:

Q: Solve the congruence 9x   21 (mod 33).

A:

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

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: 3. Find all solutions of the congruence: 19x = 7 mod 69 .Show all steps to get full credits.

A: To find the solution of given linear congruence.

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

A:

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

A: ANSWER IS 12 NON  CONGRUENT SOLUTIONS MODULO 48

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: Solve the congruences. a) 5x =7 (mod 8) b) 11x 2 (mod 6)

A:

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 3x≡2, (mod 7) or show that no solution exists.

A: We have to solve given problem:

Q: solve the following congruence equation:3x+58 ≡1(mod 12)

A: If ab≡bc(mod nb) then a≡c(mod n) And if ab≡bc(mod n) and if (b,n)=1 then a≡c(mod n)