Exercise 3. 3x +1= 2 (mod 9) a has no solution modulo 9 b. has six non-congruent solutions modulo 9 c. has a unique solution modulo 9 which is 2(mod 9) d. has only three non-congruent solutions modulo 9 which are 2(mod 9), 5(mod 9). and 7 (mod 9)

Q: (a) Solve the linear congruence 26x = 1 modulo 33

A: Solution

Q: The equation 20x=30 (mod 70) has: 10 non-congruent solutions modulo 70 None of these no solution…

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Q: Find all whole number solutions of the congruence equation.  2x+1≡ 5 mod 4 3x+1≡ 4 mod 9

A: The given problem is to find the whole number solutions for given system of linear congruence…

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: Find the smallest positive integer x that solves the congruence: 7x≡5 (mod52)

A: 7x≡5 (mod52)---(1)

Q: Find all integer solutions satisfying all the equations given. 5x =1 mod 39 3x =1 mod 25 4x =1 mod…

A: Concept :.   *   ax =6 mod n                           g (d (a,n) = d (let)…

Q: For which positive integers a is the congruence ax4 ≡ 2 (mod 13) solvable?

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Q: (9) Find all prime numbers p for which both equations X²-2 0 mod p and have solutions. X²-3 0 mod p

A: Concept: The quadratic congruence: x2≡a(mod p) , where gcd(a,p)=1 Has a solution if (ap)=1 That is a…

Q: Exercise 4.21. Prove that x2 = 1 (mod p) has exactly two solutions when p> 3 is a prime. 70

A: We shall solve it using basic knowledge from elementary number theory, in particular the properties…

Q: The least positive solution modulo 330 for the system x = 2(mod 5) x = 1(mod 6) T = 3(mod 11) is x =

A: Want  to find: The least positive solution modulo 330 for the systemx≡2 mod 5x≡1 mod 6x≡3mod 11we…

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

A:

Q: Use the index system modulo 19 to find all solutions of x3≡11(mod 19) and 5x≡4(mod 19).

A: The congruences given are as follows: x3≡11mod 195x≡4mod 19 We are asked to find the value of x that…

Q: The system 2x + 3y = 4 (mod 4) 3x + 4y = 5 (mod 4) has no solution modulo 4. Select one: True False

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Q: 5. Explain why the congruence r = 2 (mod 4) has no solutions in Z.

A: We have to show that the congruence x2≡2(mod 4) has no solution in ℤ

Q: 4. Using your work from the earlier parts or independently find: (a) mod 8 (b) + mod 23 17 (c) mod 7

A: Given

Q: 8. Find the solutions to the given system of linear congruence. x= 1 (mod 3) x = 3 ( mod 5) x = 4 (…

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Q: The equation 21x=49 (mod 70) has: 6 non-congruent solutions modulo 70 7 non-congruent solutions…

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

A: P

Q: Suppose x satisfies the three simultaneous congruences X = 4 (mod 5) x = 7 (mod 8) X 10 (mod 11)…

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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: 5) Solve the system of linear congruences below: x ≡ 6 (mod 9) x ≡ 10 (mod 13) x ≡ 18 (mod 29)

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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: (b) Prove that if a = 7 mod 10 and b = 6 mod 15, then a + b = 3 mod 5.

A: Our objective is to prove . Since you have posted multiple questions I am solving one.

Q: Find the first few terms of the sequence of pseudorandom numbers generated using the linear…

A:

Q: 2x ≡ 12 mod 5 5x + 4 ≡ 2 mod 8

A: 1) 2x = 12 mod 5  2x = (5*2 + 2) mod 5  2x = 2  x = 1  (1 is whole number)    Only 1 whole number…

Q: The equation 12x=24 (mod 48) has: * no solution modulo 48 24 non-congruent solutions modulo 48 None…

A: Given the equation 12x≡24(mod 48)

Q: You and your friend Lara are considering the linear congruence ax = b (mod m), where m = 6 x 11 x…

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Q: Find the first few terms of the sequence of pseudorandom numbers generated using the linear…

A: Given below an step by step solution

Q: Use the index system modulo 19 to find all solutions of x³ = 11 (mod 19) and 5ª = 4 (mod 19)

A: In the theory of congruence, Fermat's little theorem is very significant. It says that for any prime…

Q: Exercise 36 Prove that x? = a (mod p) has either no solutions or 2 solutions when p is a prime and a…

A: I have use the method of contradiction

Q: Find all whole number solutions of the congruence equation. 3x+12 ≡ 7 mod 10

A: The given congruence equation is                                             3x+12≡7 mod 10

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

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Q: Why does the linear congruence 25x ≡ 30 (mod 75) have no solutions?

A: To show that the linear congruence 25x≡30mod 75 have no solutions.

Q: A.)Many printed airline tickets contain a 10-digit document number followed by a check digit. The…

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Q: The linear congruences a = 3 (mod 9), x = 9 (mod 24) has simultaneous unique solution modulo .…

A: The given system of linear congruence is: x≡3(mod 9)x≡9(mod 24)

Q: 1. Find all solutions to the system of congruence. (Use CRT) x = 1 (mod 2) x = 2 (mod 3) x = 3 (mod…

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Q: Solve the system of congruences 2x + 6y = 3 (mod 15) 3x + 7y = 6 (mod 15)

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Q: Find all solutions to the congruence 10x≡5 mod 15 (b) Prove that 7 divides 32n+1+ 2n+2for any…

A: In  (a) we use the extended Euclidean algorithm to solve the problem. In (b) we use the mathematical…

Q: The equation 30x≡24 (mod 48) has: * 24 non-congruent solutions modulo 48 no solution modulo 48 None…

A: ax≡b (mod m) has solutions if and only if gcd(a,m) divides b. Moreover the number of non-congruent…

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: The equation 21x = 49 (mod 77) has: O no solution modulo 77 only 11 non-congruent solutions modulo…

A: Here we have given equation,  21x = 49 (mod 77)    Let a, b and m be integers such that m>0 and…

Q: 3. Find all integer solutions to the pair of congruences (if any) x = 1 (mod 2) x = 2 (mod3) x = 3…

A: To Find: Integer solutions to the pair of congruences(if any) x≡1(mod 2), x≡2(mod 3), x≡3(mod 5)…

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: 3 congruent to 1 (mod5) 2 congruent to 3 (mod 7) 5 congruent to 11 (mod3)

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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: 2x = 1(mod 5) 31( mod 7) 5x 9(mod l)

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Q: Solve the system of congruence x ≡ 3 (mod 6) and x ≡ 4 (mod 7) using the method of back…

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