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: 7) Show that there are no primitive roots modulo 21 using EGLF and CRT.

A: Given value of n is 21 . Now, break 21 into its factor, 21=7×3 ,7,3=1 If m>2 and n>2 then the…

Q: If mx = 1 (mod n) has a solution, then nx = 1 (mod m) has no a solution. Select one: True False

A: We know the definition of Congruence ,  Suppose m be a positive integer , we say that integers a and…

Q: Let's say that Alice and Bob are exchanging keys using Diffie-Hellman key exchange using…

A: Here, we have p=499 (which is a prime number) g=7 a=23 (which is a secret exponent of Alice) and b…

Q: Show that if p is a prime number then every equation of the form ax ≡ b mod p with a 6≡ 0 mod p has…

A: Given p is a prime number and 6≡0 mod p. Therefore either p=2 or p=3. Let d=gcda,p. We know that if…

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: Find all whole number solutions of the congruence equation.  2x+3 ≡ 8 mod 12

A: # we are entitled to solve one question at a time . Please resubmit the other question if you wish…

Q: Take the last four digits ABCD of your student identification number, and let AB and CD be the…

A:

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: Find the sequence of pseudorandom numbers generated by the linear congruential method with modulus m…

A: Given that, the recurrence relation is xn+1=axn+c mod m, and m=9, a=89, c=2 and x0=5. Obtain the…

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

A:

Q: . (a) How many quadratic residues are in the residue set Z19? (b) Determine if 4 and 9 are quadratic…

A: Introduction: Quadratic residue is a part of congruent modulo theory. It is a non-linear congruence.…

Q: 1. Suppose we build an LFSR machine that works mod 3 instead of mod 2. It uses a recurrence of…

A:

Q: Consider the pseudorandom number generator given in our lessons: with Uf +1 = (auf + b) mod m…

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

A: Given

Q: Solve the congruence3x−7 = 2 (mod 16). Your solution should be positive and reduced modulo16.

A:

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

A:

Q: solve the congruence of  6x=4 mod 10  aolve the conguence of 341x=2941 mod 9

A:

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

A: P

Q: Find the sequence of pseudorandom numbers generated by the power generator with p = 11, d = 2, and…

A:

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

A:

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: The linear congruence 9x = 19 (mod27) has 3 incongruent solutions. :Select one True False

A:

Q: What sequence of pseudorandom numbers is generated using the linear congruential generator r1= (4r,…

A:

Q: Suppose Alice and Bob have the same RSA modulus n and suppose that their encryption exponents eд and…

A:

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

A:

Q: I know that using a corollary that the congruence x2 ≡ 0 (mod p) that the only solutions are + and -…

A: As per the question we have the following congruence relation : n ≡ 2(mod 4) And we have to prove…

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: Using Fermat's Little Theorem 62003 (mod 11) Compute the last two digits of…

A:

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: (b) Give an example of a composite integer n such that the congruence x =1 (mod n) pas more than two…

A:

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

A: We have to find few terms of the given sequences.

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

A:

Q: If mx = 1 (mod n) has a solution, then nx= 1 (mod m) has a solution. Select one: O True False

A:

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

A:

Q: Find all solutions of quadratic congruence x^2+85x+2=0(mod401)

A: We follow the method of completing the squares of the equation x^2+85x+2. Note that 85 is odd so we…

Q: 6. What sequence of pseudorandom numbers is gener- ated using the linear congruential generator xn+1…

A: Given: Linear congruential generator xn+1=4xn+1 mod 7, with x0=3 To find: Sequence of psedorandom…

Q: Use Wilson's Theorem to prove that for primes p congruent to 1 modulo 4 the quadratic congruence 1'…

A: Given The quadratic congruence x2≡-1(mod p) To prove  x2≡-1(mod p) has a solution if p≡1(mod 4)…

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

A:

Q: Which are true for modulo 12? 1.) Does 5x ≡ 6 mod 12 have a solution? How many? 2.) Does 4x ≡ 6 mod…

A:

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: Number theory

A:

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

A:

Q: (b) Solve the set of congruences 2x =1 (mod 5) x=3 (mod 4)

A: Note:- We’ll answer the first question according our protocol. Please submit a new question…

Q: Find the smallest positive integer xx that solves the congruence: 11x≡5(mod57)

A: