Find all solutions mod 31 to the congruence x° = -5 (mod 31).

Q: Use this theorem to solve the following congruences: x1 = 13 mod 35

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

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

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Q: Find all solutions of the congruence x2 ≡ 29 (mod 35).

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Q: Solve each of the following congruences. (a) 6x + 3 = 4 mod 10 (b) 6x + 3 = 1 mod 10 (c) x² = 1 mod…

A: In congurent modulo n, ax≡bmod n has exactly 'd' solutions if 'd' divide 'b'where d=gcda,n otherwise…

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

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Q: (c) Find a value t modulo 7 so that (3+ 7t) does not solve the congruence x® – 1 = 0 (mod 49).

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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: {-74 + 1, ..., 74 – 1}. (b) Hence, find a solution to the congruence x' = 99 mod 74.

A: Given:- An expansion above Polynomial will have co-efficient lies between {-74+1,..........,74+1}

Q: 5x = 7 (mod 32)

A: To solve the following problem

Q: 3. Solve each of the following congruences. (a) 6x + 3 = 4 mod 10 (b) 6x + 3 = 1 mod 10 (c) x² = 1…

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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: Solve the following linear congruence: 17 x congruence 3 (mod 210)

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Q: Solve the congruence x? = 79 mod91.

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

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Q: 1. Find all solutions to the following congruences. (a) 2x +3 = 7 (mod 9) (b) 2x +3 = 7 (mod 20) (c)…

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Q: Find all incongruent solutions - if exist - for the congruence: 36x = 96 mod 156

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Q: Use this theorem to solve the following congruences: (1) x° = 2 mod 35 (2) x' = 13 mod 35

A: Since you have asked multiple questions, we can solve first question for you. If you want other…

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

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

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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: Give all the integer solutions of the congruence 56x-12=0 (mod 23).

A: Given congruence 56x-12 ≡ 0 (mod 23) i.e., 56x ≡ 12 (mod 23) i.e., 10x ≡ 12 (mod 23) We know that,…

Q: Find all solutions, if any, to the system of congruences x ≡ 7 (mod 9), x ≡ 4 (mod 12), and x ≡ 16…

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Q: 2. Find all solutions, or show there are none, to the congruence X78 = 5 (mod 19)

A: By Fermat little theorem x18≡1mod19. Therefore, x4×18+6≡x6mod19 or x78≡x6mod19.

Q: Using Fermat's little theorem, find the solutions of the following linear congruences. a) 7x ≡ 12…

A: Fermat's theorem :  Let p be prime number such that gcd(a,p)=1 then ap-1≡1(mod p) Using Fermat's…

Q: Find all solutions, if any, to the system of congruences x ≡ 5 (mod 6), x ≡ 3 (mod 10), and x ≡ 8…

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

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Q: Solve the following linear congruence. 5x = 2 (mod 26).

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Q: -) Find the solutions, if any, of each congruence. 21x 10 (mod 35) 9x = 15 (mod 21).

A: We know that, ax≡b mod n has solution if and only if gcd(a,n) divides b.

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

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

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

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Q: 3

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Q: A sequence of pseudorandom numbers is generated as follows Xo = 4 x₁ = ( 6x₁-1 + 5 ) mod 13 if i > 0…

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Q: Solve the following linear congruence: 6x = 15 (mod 21).

A: We Know that the congruence ax = b (mod n) has a solution if and only if d = (a, n) divides b. If…

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: solve by means of a derivation, the congrucnce equation; 10x= 4 (mod 2a) Express ansurer in form X=…

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

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Q: solution to the congruence equation (3x + 12) = 7 mod 10

A: Given :  3x+12=7mod 10⇒     3x=7-12 mod 10⇒     3x=-5 mod 10⇒     3x=5 mod 10        -5 mod 10 =5⇒…

Q: Does

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Q: The equation 12x=24 (mod 48) has: O 24 non-congruent solutions modulo 48 6 non-congruent solutions…

A: To find- The number of solutions for the given equation.

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: c. Find all non-congruent solutions to x? = 1 (mod 15) d. Find all non-congruent solutions to x2 = 4…

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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. Find all solutions to the following congruences. (d) 5x = 10 (mod 20)

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

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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)