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

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).

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

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Q: {X = I (mod 3) 2X= 2 (mod 5)

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

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Q: If gcd(a, n) = 1, then the congruence ax = b modn has the solution x = - ba®(n)-1

A: Given that gcd(a,n)=1. We need to check whether ax≡b mod n has the solution x=ba∅(n)-1

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

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

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

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

A:

Q: 3. Solve the system of congruences x = 1(mod 5) x 2(mod 6) r= 3(mod 7)

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

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Q: 5x = 7 (mod 32)

A: To solve the following problem

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

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

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Q: Solve the system of congruence x ≡ 3(mod6) and x ≡ 4(mod7) using the method of back substitution.

A: System of congruence equations

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

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Q: 11. Solve the congruence 4x = 5 (mod 9).

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

A: The congruence could be written as,

Q: 4.2 Linear Congruences 161 6. For which integers c, 0 sc< 30, does the congruence 12x =c (mod 30)…

A: Q6 asked and answered.

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: 6), then the congruence has a unique solution modulo p. 11. Show that the congruence x³ = 3 (mod 19)…

A: 11. To prove that the congruence x3≡3 mod 19 has no solutions, whereas x2≡11(mod 19) has three…

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: 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: ind all solutions of the linear congruence: 9x = 5 mod (14)

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

A: Given congruence is x2≡9 mod 600

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

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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: Solve the system of congruence's x = 2 (mod 3), x = 4 (mod 5), x = 1 (mod 7)

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Q: 3

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Q: 10. Use Euler's Theorem to show that 5P(16), '=1 (mod 16). Show your work or explain your reasoning…

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

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Q: Solve the following quadratic congruence equations 6?^2 + 13? + 7 ≡ 0 mod 17

A: The quadratic congruence ax2+bx+c=0modp can be reduced to y2= d modp where y=2ax+b and d=b2-4ac also…

Q: 9. Use Euler's Theorem to show that 3P(26). =1 (mod 26). Show your work or explain your reasoning…

A: To show it by Euler's theorem :-

Q: Solve the linear congruence 5x = 3 (mod. 11). (Show all the work.)

A: The expression, a≡b (mod c)  implies that c divides a-b, that is when c divides a-b the remainder is…

Q: Does

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Q: The linear congruences x = 3 (mod 6), x = 9 (mod 15) has simultaneous unique solution modulo. .....…

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Q: Find all whole number solutions of the congruence equation. 4x+6 ≡ 5 mod 8

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Q: How do I use the Chinese Remainder Thm. to solve this system of congruences?? x ≡ 2 (mod 3) x ≡ 6…

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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: 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: B. Solve the system of congruence's x = 5 (mod 2), x= 7 (mod 5), x= 3 (mod 7)

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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…

A:

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.