Solve the congruence: 6x ≡ 4 (mod10)

Q: Solve linear congruence 45x ≡ 60 (mod 75)

A:

Q: (Adapted from Richardson problem Solve the congruence 589z = 494 (mod 817). Hint: The solution…

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Q: Solve the congruency by finding the inverse: 7x = 9(mod 43)

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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: 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: Find all values of x (using congruent notation) for 35x ≅ 3 (mod 89)

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

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Q: Take the last four digits ABCD of your student identification number, and let AB and CD be the…

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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: Which of the following linear congruence has 1 incongruent solution? (a) 3x = 9 (mod21) (b) 14x = 12…

A: The solution is given as

Q: Which of the following linear congruence has 2 incongruent solutions? (a) 3x = 9 (mod21) (b) 14x =…

A: to solve linear congurence , ax≡b(mod m) .........(1) the first stem is to reduce the congurence  by…

Q: Solve 57x ≡ -3 (mod 50) for x

A:

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: 5x = 7 (mod 32)

A: To solve the following problem

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

A: Linear congruence

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

A:

Q: 5. Solve the congruence 11x = 15 (mod 20). (Write all solutions)

A: we have to solve                                      11x≡15(mod 20) greatest common factor of 11…

Q: Solve the congruence x? = 79 mod91.

A:

Q: Solve the following linear congruence: 36x = 8 (mod 102).

A: The linear congruence ax ≅b(mod m) has a solution iff d|b where d=(a, m)

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: Solve the congruence x² = 79 mod91.

A: The given problem is to solve the given quadratic congruence equation. Given congruence x2=79(mod…

Q: 6. Find all incongruent solutions to each congruence. Show your steps. (a) 135x = 108 (mod 612) (b)…

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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: Solve the congruence x² +1 = 0 mod 13°.

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Q: Number theory

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

A:

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: 5. Solve the following quadratic congruence using the "completing the square" method: 9x² +66x +49 =…

A: 5. Given equation is 9x2+66x+49≡0(mod 79)   To Solve: Above quadratic congruence using the…

Q: he solution of the linear congruence 103x = 444 (mod 999) is ) 111 ) 222 2 333 ) 444

A: We have to find x such that  103x = 444(mod 999)

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

A:

Q: Solve the congruence x² = 9 (mod 600).

A: Given congruence is x2≡9 mod 600

Q: Give all non-negative solutions for 10r =-17 mod 4.

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

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

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Q: Solve the following linear congruence. 36x = 8 (mod 102).

A: On solving ,we get

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

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Q: . Find a solution x € Z, 0 <x <n, for the congruence 57x + 7 = 78 (mod 53).

A:

Q: Solve the linear congruence 74x ≡ 7 (mod 69).

A: 74x ≡ 7  (mod 69).

Q: Solve the congruence 2² +1 =0 mod 133.

A:

Q: Solve the following congruences. a) 5x = 1 (mod 13) b) 12x = 40 (mod 88)

A: Given: To explain the given statement as follows, We need to solve the following congruences  5(x) =…

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

A: ANSWER IS 12 NON  CONGRUENT SOLUTIONS MODULO 48

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 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)

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.