1. Find all simultaneous solutions of the congruences: (a) X= 3 mod 5 x= 4 mod 6

Q: Solve the following congruences: (a) 3x  8 (mod 5) (b) 3x  8 (mod 12)

A:

Q: Find all the solutions of the congruence equation x6-2x5= 35 (mod 6125).

A: Consider the given congruence equation. x6-2x5≡35mod 6125. Now, the prime factorization of 6125 is:…

Q: Find all solutions for x, up to congruence.  x ≡ 2^63 (mod 61).

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Q: Solve the quadratic congruence, 6x²-7x+2 ≡ 0 mod 31.

A: We have to solve the above quadratic congurence.

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

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

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

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Q: 4. Solve each of these congruences using the modular inverses found in the previous problem. (a) 7x…

A: The given congruence equations are (a)    7x=2 (mod 26) (b)   19x=4  (mod 141)

Q: Find all four solutions to x2 =6 (mod 19 x×23) with 1<x< 437.

A: Solution:-

Q: 4. Solve the following quadratic congruences: 5x² + 6x + 1 = 0 (mod 23)

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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: Find all solutions to the following quadratic congruences by first making the leading coefficient 1…

A: Topic:- algebra

Q: Find all solutions for x, up to congruence. (b) x ≡ 11 mod 142 and x ≡ 25 mod 86.

A: Given: (b) x≡11 mod 142 and x≡25 mod 86 To find: All solutions for x, up to convergence.

Q: Solve the following quadratic congruences: (a) 3x² + 9x + 7 = 0 (mod 13) (b) 5x² + 6x + 1 = 0 (mod…

A: According to Q&amp;A guidelines, I can answer only one question. So I answered (a).

Q: Find the solutions of the congruence 15x2 + 19x ≡ 5 (mod 16).

A: Congruence modulo relation on integers:Let a,b∈Z and let m be a fixed positive integer. Then we say…

Q: (2x + 3 ) ≡ 8 mod 12

A: (2x + 3 ) ≡ 8 mod 12 x + 3 + 9 ≡ 8 +9 mod 12  2x + 12  ≡ 12 +5  mod 12

Q: 2. Find all solutions of the linear congruence 12x = 9 (mod 15).

A: P

Q: Find the solutions of the congruence 15x2 + 19x ≡ 5 (mod 65)

A: The given equation is: 15x2+19x≡5(mod 65)

Q: Use Hensel's Lemma to find a solution to the following congruence: a +3 x + 3 = 0 mod 54.

A: Let f(x) be a polynomial , p is a prime number . If x=a is a solution of congruence equation…

Q: Find all whole number solutions of the congruence equation. (2x + 1) ≡ 5 mod 4

A: Consider the given congruence equation. (2x + 1) ≡ 5 mod 4

Q: Q-2: a) Find the set of solutions of each of the linear congruence: i. x = 3 (mod 5). 5 (mod 9). ii.…

A: The solution is given below

Q: Find all the solutions to the linear congruences  (b) 128x = 833 mod 1001 (c) 36x = 30 mod 42

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

A:

Q: If possible, find a complete set of mutually incongruent solutions of each of the following…

A: The given congruences, a) 9x≡12mod 15. b) 81x≡57mod 117. We have to find the solution to the…

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

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

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Q: ) Find all primitive roots modulo 7.

A: We have to find all primitive root modulo 7.

Q: 2. Solve the simultaneous congruences x = 4 (mod 5) and 2x = 3 (mod 7)

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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: linear congruence has 2 incongruent solutions

A: b is correct. We have to find out the total number of solutions of the given linear congruence.

Q: tind all ins ongrnent solution the cangruence i¥ exist for 36X= 96mod 156

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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 following equations in Z, giving full details of your analysis (a) 5x + 3 = 1 (mod 6) (b)…

A: We have to solve the equation in

Q: Find all solutions to the following quadratic congruences by first making the lead coefficient 1,…

A: