Fill in the values in the algorithm of fast exponentiatic 520 mod 7 = 5' mod 7 = 5 522 mod 7 = Ex: 8 2 mod 7 = Ex: 8 52 mod 7 = Ex: 8 2 mod 7 = 2 523 mod 7 = 22 mod 7 = 4 12 mod 7

Q: When all the numbers in a given data series appear only once, then the series is said to: a. be…

A: We know that, Mode:     The value occurs with the highest frequency. Uni mode: When there is only…

Q: 11 4 Solve 11 divided by 4 in the algorithm. 4) RO 4 1 -

A: Now we will solve the problem

Q: Please prove that: (р —q) —>r and p > (q > г) equivalent. Use Equivalent algorithm

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Q: The number 0.60 is rational and can be represented in finitely many digits in decimal  a. can it be…

A: Questions regarding the binary representation of 0.6

Q: Find the least residue of 63^9 modulo 10

A:

Q: Find 96307 7 (mod 739) using the techniques described in Example 8.4.4 and Example 8.4.5. First…

A: To find 96307mod739. It can be computed by evaluating the following,…

Q: Fill in the values in the algorithm of fast exponentiation: 220 mod 5 = 2' mod 5 = 2 221 mod 5 = Ex:…

A:

Q: Find the inverse ā of 5 modulo 187 using (extended) Euclidean Algorithm with 1 <a< 186.

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Q: Find the inverse of 17 mod 26 by using Euclid's Algorithm?.

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Q: 1. How many solutions( mod 419) does x = 186 mod 419 have? (Show your work!) 2. How many solutions (…

A: Given: x2≡186 mod 101 We need to solve x2≡186 mod 101 and how many solution exists.

Q: Use 672 = -1 mod 449 and Hermites' algorithm to find a pair of positive integers s and t such that…

A: Given :          s2 +t2 = 449672 = -1 mod449

Q: Use Euclid's Algorithm to find a multiplicative inverse of 23 mod 75. Once found, solve the linear…

A:

Q: 6. Use Fermat's little theorem to compute : 3302 mod 7.

A:

Q: Using Euclid's Algorithm, what is a multiplicative inverse of 23 mod 75 and then solve 23x is…

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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: 3) Use the Euclidean algorithm to find (662,488) and express it as a linear combination of these…

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Q: Determine the classification of error when a mod- eler uses a numerical optimization technique in…

A: Follow the steps.

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

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Q: Use Fermat's Little Theorem to find (Show work.) a) 945 mod.23. b) 231002 mod. 41 c) (-9)933 mod. 13

A: Fermat's Little theorem states that " if p is a prime number and a is not divisible by p then…

Q: solve for x^2 = 1 mod 8 and x^2 = 1 mod 10

A: Solution...

Q: Use the Euclidean Algorithm to find ?=gcd(4753,1379) and express ? as an integral linear combination…

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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: Apply the Extended Euclidian Algorithm to find 1/21 modulo 59 with a table

A: We will apply Extended Euclidian Algorithm to find 121 modulo 59 i.e., multiplicative inverse of 21…

Q: 6. Trace Algorithm 4 when it is given m = 7, n = 10, and b = 2 as input. That is, show all the steps…

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Q: A common method for calculating the check digits for credit cards is called the Luhn algorithm.…

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Q: Write an algorithm in pseudocode for generating a sequence of pseudorandom numbers using a linear…

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Q: Fermat's "Little" Theorem states that whenver n is prime and a is an integer, d"-1 = 1 mod n a) If a…

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Q: Let a, k and n be positive integers. Describe a fast algorithm to compute ak MOD n. Illustrate your…

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Q: Find the inverse of 17 mod 26 by using Euclid's Algorithm?

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Q: A certain computer algorithm executes twice as many operations when it is run with an input of size…

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Q: What sequence of pseudorandom numbers is generated using the linear congruential generator Xn+1 =…

A: Given that xn+1=(3xn+465)mod 8191x0=1

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: Calculate the least residues modulo 5 of 14, 24, 34, and 44.

A:

Q: Fermat's "Little" Theorem states that whenver n is prime and a is an integer, d"-1 = 1 mod n a) If a…

A: Given, Fermat's Theorem :- If n is a prime number and a denotes an integer such that a,n=1, then…

Q: Use the Euclidean Algorithm to determine if 7^-1(mod 20) exists.

A: To determine if 7-1mod 20 exists, using Euclidean Algorithm.

Q: please do 5

A: (a) Use the Euclidean algorithm to find the GCD as follows.

Q: 2. Write an Algorithm to check a number and print if its even or odd. (Specify input, output and the…

A: We need to print if the given number is even or odd. The basic definition of even number is it is of…

Q: What sequence of pseudorandom numbers is generated using the linear congruential generator xn+1 =…

A: According to the given information, it is required to find the sequence of pseudorandom numbers.

Q: gcd (40489, 76397) by euclid's algorithm

A:

Q: Suppose that 3x ≡ 2 (mod 5). Find the remainder when x is divided by 5; in other words, compute x…

A: ANSWER :

Q: Illustrate the key ideas in the proof of correctness for Prim's Algorithm.

A: As per the question we have to explain the proof of correctness for the Prim's Algorithm In terms of…

Q: Find a such that 5= 7* modulo 13.

A: Given: 5≡7xmodulo13. The objective is to find the value of x.

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: 3 . Use the baby-step giant-step algorithm to find h, k such that 2^h ≡ 7 (mod 53), 2^k ≡ 9 (mod…

A:

Q: A certain computer algorithm executes twice as many operations when it is run with an input of size…

A: Given The algorithm executes twice as many operations when the input size is k as when it is run…

Q: Find 75307 mod 735 using the techniques described in Example 8.4.4 and Example 8.4.5. First compute…

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Q: Fill in the missing numbers of the sequence generated by Euclid's algorithm on inputs 58 and 10.…

A: As per Euclid' Algo: gcd(a,b) 1. If a = 0, then b is gcd.  2. If b = 0, then a is gcd 3. If both are…

Q: Use Newton's method to determine which algorithm can be used to compute v6. In+1 = 6 3z, + In In+1…

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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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