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

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

A: The solution is given below

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Q: The sum of the first n odd numbers is n°; that is, Ź(2x – 1) = n². X=1 Verify this formula for n =…

A: The sum of the first n odd numbers is n2. Then we get, ∑x=1n2x-1=n2 We have to verify the results…

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

A:

Q: (1) Consider the equation 2.x +1 = 0 mod n. For which n are there no solutions? one solution?…

A: Congruence

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

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Q: In 7 + 4√3 2.63391 ≈

A: The given expression is  ln7+43

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: Find all solutions to x^2=6 mod 143, note that 143=11*13 (I solved x^2=133 mod 143, but i'm not sure…

A: It is required to find all the solutions of x2=6mod143 Given that 143=11×13 Where 11 and 13 are…

Q: 2. Solve For O40127 4cose=CO50+3

A: The given equation is;  4cos(theta/2) =cos(theta) +3.

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: Solve : ex+ay =4 (mod 13) E 2 2 (mod 13) Using elimination

A:

Q: Solve the following equation modulo 5.  2x=3

A: Given that 2x=3(mod5)    equation (1) We known that 0x= 5(mod5)   equatiion (2)

Q: (3) If today is Thursday what day of the week will it be 31 days from today? (4) If it is currently…

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

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Q: Solve for x. 5+ In (x – 2) = 4 Do not round any intermediate computations, and round vour answer to…

A: Finding x

Q: Solve for x € Z9: 215x = 4524 (mod 9)

A: We know that linear congruence is of the form ,  ax ≡ b mod m  ,  where a , b , m are integers and m…

Q: Solve for x : 5x ≡ 7 (mod 6).

A: Here remainder is 7 and modulus is 6 we can write it as  5x-7 =6n          Where  is an positive…

Q: solve the congruence of  6x=4 mod 10  aolve the conguence of 341x=2941 mod 9

A:

Q: Find all the solutions r E Ziz to the equation r³ – 5x² – 7x = 0 mod 13.

A: First, solve in real number then ring down to the finite field.

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

A:

Q: Q4 (a) Solve for x if 25x = 15(mod 29). (b) Determine the smallest positive integer so that when…

A:

Q: solve 2x 1(mod13)

A: We are given that 2x≡1(mod 13) ⇒2x-1 is divisible by 13. Consider , 2x-1=13m , where m∈Z ⇒x=13m+12,…

Q: Solve for x. 3 In (x+1) = 15 Do not round any intermediate computations, and round your answer to…

A: Given: 3lnx+1=15

Q: Solve for x using a =b mod m) iff mlla-b): 8 I lx-19)

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

A: Given congruence is x2≡9 mod 600

Q: Solve xS+x*+l =o (mod 34)

A: Given :                        x5 + x4 + 1 ≡ 0 (mod 34)             First, we solve it mod 3.…

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

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Q: Find all solutions for 10x = 14 mod 1008

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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: 5. (8x*y® + 3x³) dx + (12x°y³ + 3xy²) dy = 0

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Q: 3.2.6 Find all solutions x to the congruence equation 12x = 1 (mod 17)

A: Given, 12x = 1 (mod 17) So, 7•12x = 7•1 (mod 17) So, 84x = 7 (mod 17)

Q: Number theory

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Q: 10. Find the sum of all incongruent solutions of a =1 (mod 17). (Enter the least non-negative…

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Q: Solve x 3D 1(mтod4) x = 3(mod6)

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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: 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: 1)For each of the following, find an integer value x which satisfies the equation, or explain why…

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Q: Solve for a a ≡ 13 mod 5353

A: To solve  a ≡ 13 mod 5353

Q: 6. Find a prime number p for which the equation x² = -1 mod p has no solution.

A: Given is a  modular equation.   To Find: A prime number p such that the given equation has no…

Q: Solve. In (x + 4)' + 13 = 27 If the answer is not an integer, enter it as a decimal. Round to the…

A: We have to solve

Q: Solve the Diophantine equation 7x + 5y = 43 by  rst solving the congruence 7x = 43 (mod 5), which is…

A: