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

Q: Given 6x + 2 ≡ 101 (mod 7), find an integer z such that 2x ≡ z (mod 7)

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

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Q: 2n-1 b) Prove that if , r #1 (mod 2"), then n is even.

A: Given that x2n-1≢1mod2n . The objective is to show that n is even. The x2n-1≢1mod2n can be written…

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

A:

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

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Q: How many square roots of 3 (mod 1001) are there? (Hint: 1001 = 7 * 11 * 13)

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Q: Find the common solutions to the congruences 2x 3x 1 (mod 5) (mod 6) 1 (mod 7). 9 4x

A: Given : 2x≡1 (mod 5)3x≡9 (mod 6)4x≡1 (mod 7) To find : The common solutions to the congruences.

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

A:

Q: Given a = 4( mod 9) and b = 5( mod 9), find c with 0<c<9 such that c = 5a + 3b ( mod 9)

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Q: a) Find all solutions to the congruence 10r = 5 mod 15

A: Given,

Q: Using Chines Reminder Theorem, Solve the congruence x = 4 (mod 13) x = 5 (mod 11) х 3 11 (тоd 15)

A:

Q: 5x = 7 (mod 32)

A: To solve the following problem

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: Number theory

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Q: 4. (a) Solve the set of congruences х 1(mod 3), x= 2(mod 4), x = 3(mod 5).

A: We  will solve it by Chinese Remainder Theorem Given  x≡1(mod3)x≡2(mod4)x≡3(mod5) Compare it with…

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

A:

Q: Write the set of solutions of x=5 (mod 24) x= 17 (mod 18), if any as the solutions to a single…

A: We have a set of congruence as x ≡ 5 (mod 24)x ≡ 17 (mod 18) From the first equation we can write…

Q: b) Determine whether or not x? = 85 (mod 97) has a solution.

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Q: 11) The solution of the linear congruences x = 1 (mod 2), x = 2 (mod 3), x = 3 (mod 5), x = 4 (mod…

A: We have to find value of x

Q: Find the value of x if any. Show your complete solution. 1.   (13 + x) = 3 mod 16 x = 2.   (3x +…

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Q: Consider modulo 11. a. Find 35 mod(11). b. Find a negative integer x such that x mod(11) is…

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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: -) 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: 24. Given the linear congruence (16x is congruent to 72 mod 24.) How many possible incongruent…

A: 24. To find the number of incongruent solutions of16x≡72mod 24

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

A: Given congruence is x2≡9 mod 600

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: (b) Let x be an integer such that 0 < x < 8 and (10500 + 105000 ) = x (mod 9). Justifying your…

A: We have to find the required value of x .

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

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Q: Find an integer x that satisfies the equation. 5* = 4(mod 11) 17x?=10(mod 29) i. %3D ii.

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Q: Give an example to show that a ^2 ≡ b^2 (mod m) need not imply that a≡ b (mod m)

A: Here I listed given example of above statement.

Q: Find all the whole number solutions of the congruence equation. 3x 8 ≡ mod 11 3x + 12 ≡ 7 mod 10

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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: True/False: If 10x = 20 (mod 8) holds, then x = 2 (mod 8) must be true.

A: True.

Q: mod 32, given Xo=1 Please answer w

A: The congruential generator is given as:Xi+1 = 11Xi mod 32, where we are given X0 = 1. We see that,…

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: Exercise 5 Find all integer solutions to the following equations. (1) a? =5 (mod 312). (2) a? – 4x +…

A: 1  The equation can be written as: x2=5x=±5x=5   or  x=-5. Hence, there will exist two real value…

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

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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: 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: Use the repeated squaring method to calculate the following: 16^10 (mod 230)

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Q: The equation 12x=24 (mod 48) has:

A: ANSWER IS 12 NON  CONGRUENT SOLUTIONS MODULO 48

Q: x = 13 (mod 39) have a solution. Select one: O True 2.

A: True

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

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

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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: Exercise 32 Solve the following equations: 1. 3x = 5 (mod 7).

A: Dear Bartleby student,according to our guidelines we can answer only three subparts, or first…