Find the first few terms of the sequence of pseudorandom numbers generated using the linear congruential generator Xn+1 = (2xn + 5) mod 8 with seed xo 5? X2 = X3 = X4 = X5 = = 9x Now find the first few terms of the sequence of pseudorandom numbers generated using the linear congruential generator Xn+1 = (4xn + 2) mod 9 with the seed xo = = 3? X2 = X3 = X4 = X5 = = 9x

Q: What is the number of solutions to the congruence in Z125? x³ + x² + 3 = 0 (mod 125)

A: As per the question we have to solve the following polynomial congruence equation : x3 + x2 + 3 ≡ 0…

Q: 2. Euclidean Algorithm Use the Euclidean algorithm to find gcd(12345, 678).

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Q: x^2 ≡ 1 (mod 105)

A: Given: x2≡1(mod 105) To Solve: The given congruence  x2≡1(mod 105)

Q: Find all solutions of the congruence 8x ≡ 4 (mod 12)

A: Step 1: Divide by the greatest common divisor (GCD)The GCD of 8 and 12 is 4. We can divide both…

Q: (i) Count the number of bit strings of length four that do not have two consecutive 1s?

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Q: 5x = 8 (mod 2) 7x = 3 (mod 5)

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 2r = 3 4x = 2 3x 2 (mod 5) (mod 6) (mod 7).

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Q: Prove that if ax = b (modn) then () x = () (mod ()) where d = gcd(a, n). Apply this result to 5x =…

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Q: Without performing the divisions, determine whether the integers 176521221 and 149235678 are…

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Q: Compute the 3^201 mod 5.

A: Congruence value

Q: 3. Find the following: A. 3^0 mod 5 1 B. 3^1 mod 5 3 C. 3^2 mod 5 1 D. 3^3 mod 5 4

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Q: Solve the system 3x + 2y = 5 2x + 7y= 9 mod 17 mod 17

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Q: (73 – 98)(mod 3) = (mod 3)

A: GIiven, a expression using modulo function.

Q: Compute the addition modulo operation 3+2 2 0. 1 3 O O

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

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

Q: How could we calculate the congruences 10^x ≡ 243 mod 19^2 with 14x^15 ≡17 mod 19. The answer of mod…

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Q: x43 = 47 (mod 713)

A: Step:-1 By Chinese remainder Theorem (CRT),  x43 ≡ 47 mod 713 if and only if x43 ≡47 mod 23 ⇒x43 ≡1…

Q: Solve the system of congruences 2x ≡ 1 (mod 5) 3x ≡ 9 (mod 6) 4x ≡ 1 (mod 7) 5x ≡ 9 (mod 11) Hint:…

A: We can solve this system of congruences using the Chinese Remainder Theorem. First, let's write each…

Q: Compute 17^7121 (mod 11).

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Q: Which of the following linear congruence has no solution? (a) 3x = 9 (mod21) (b) 6x = 4 (mod20) (c)…

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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: 3. Solve the system of congruences x = 1(mod 5) x 2(mod 6) r= 3(mod 7)

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Q: If x = 2 (mod 5) and y = 4 (mod 5) then 2x – 3y =? (mod 5)

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Q: 2) Find 281171 + 171281 (mod 12)

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

A: Topic:- algebra

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

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Q: Find the least positive integer n that satisfies the congruence 7 ^128 congruent to n (mod13)

A: Given, 7128≡nmod 13 Find the value of n that satisfies the above congruence.

Q: Find the roots of the characteristic equation of the following homogeneous ODES: (a) yll +yl + y = 0…

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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: (13),0 - (159), using excess-3 codes with 9's complement method.

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Q: solve the quadratic congruence 7x^2 - 8x +4 = 0 (mod 17)

A: The given problem is to solve the given quadratic congruence equation 7x2-8x+4 = 0(mod 17)

Q: If a≡3 (mod 11) and b≡9 (mod 11): (a) Compute a+b(mod 11) (b) Compute a^3(mod 11)

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Q: Simplify (42-67)(mod 3). (42-67)(mod 3) = (mod 3)

A: Here we have to find the value of(42-67)mod 3

Q: Please help!

A: Solution is given below

Q: . Find all the solutions of 3x² + 2x + 1 8 (mod 63).

A: Given a quadratic congruence in the form:Ax2+Bx+C=0(mod n)multiply the above equation by…

Q: I have a message 2,3,6,5 (mod.7),  I will find a check digit by multiplying the first and third…

A: Here, First number= 2 Second number =3 Third number= 6 Fourth number= 5

Q: Solve the system of congruence x ≡ 3(mod6) and x ≡ 4(mod7) using the method of back substitution.

A: System of congruence equations