NUMBER THEORY 1.Use the Euclidian algorithm to calculate the GCD of 1160718174 and 316258250. 2.Use Fermat’s...

NUMBER THEORY

1.Use the Euclidian algorithm to calculate the GCD of 1160718174 and 316258250.

2.Use Fermat’s Little Theorem to solve for x^86 ≡ 6 (mod 29).

Expert Solution

Colby Messinger answered 2 years ago

Find the GCD (5796852, 4585268) using the Euclidian Algorithm..

We also discussed the use of the Extended Euclidian algorithm to calculate modular inverses. Use this...

We also discussed the use of the Extended Euclidian algorithm to calculate modular inverses. Use this algorithm to compute the following values. Show all of the steps involved. 9570-1(mod 12935) 550-1 (mod 1769)

NUMBER THEORY 1.Find all the possible solutions for the following diphantine equations by using the euclidian...

*NUMBER THEORY* 1.Find all the possible solutions for the following diphantine equations by using the euclidian algorithim. You must show all the process to get credit. a. 3x + 5y = 7 b. 3x − 12y = 7 c. 1990x − 173y = 11 d. 21x + 48y = 6 e. 2x + 3y + 5z = 11

Find the largest number of divisions made by Euclid’s algorithm for computing gcd(m, n) for 1≤...

Find the largest number of divisions made by Euclid’s algorithm for computing gcd(m, n) for 1≤ n ≤ m ≤ 100.

Sample Execution : Recursive Euclidean Algorithm to calculate GCD Type a positive integer for...

Sample Execution : ** Recursive Euclidean Algorithm to calculate GCD ** Type a positive integer for A: -2 Sorry, you must enter a positive integer (>0). Please try again. ** Recursive Euclidean Algorithm to calculate GCD ** Type a positive integer for A: 35 Type a positive integer for B: 63 The GCD is 7 Write a MIPS assembly program that prompts the user for 2 positive integers (>0). Then it uses the Recursive Euclidean Algorithm to calculate GCD (the...

Use the Euclidean algorithm to find the GCD of 3 + 9i and 7-i

a. Using the Euclidean Algorithm and Extended Euclidean Algorithm, show that gcd(99; 5) = 1 and...

a. Using the Euclidean Algorithm and Extended Euclidean Algorithm, show that gcd(99; 5) = 1 and find integers s1 and t1 such that 5s1 + 99t1 = 1. [Hint: You should find that 5(20) + 99(?1) = 1] b. Solve the congruence 5x 17 (mod 99) c. Using the Chinese Remainder Theorem, solve the congruence x 3 (mod 5) x 42 (mod 99) d. Using the Chinese Remainder Theorem, solve the congruence x 3 (mod 5) x 6 (mod 9)...

1. Calculate gcd(181451, 186623). 2. For integers a, b, and c, if a | bc, then...

1. Calculate gcd(181451, 186623). 2. For integers a, b, and c, if a | bc, then either a | b or a | c.

Write an algorithm to input a number n, then calculate 13 +2 3 + 33 +...

Write an algorithm to input a number n, then calculate 13 +2 3 + 33 + ... + n3, the sum of the first n cubic numbers, and output the result. 2-Construct a trace table of the algorithm in question 1 with input n=4.

Question

NUMBER THEORY 1.Use the Euclidian algorithm to calculate the GCD of 1160718174 and 316258250. 2.Use Fermat’s...

Solutions

Expert Solution

Related Solutions

Find the GCD (5796852, 4585268) using the Euclidian Algorithm..

Find the GCD (5796852, 4585268) using the Euclidian Algorithm..

We also discussed the use of the Extended Euclidian algorithm to calculate modular inverses. Use this...

NUMBER THEORY 1.Find all the possible solutions for the following diphantine equations by using the euclidian...

Find the largest number of divisions made by Euclid’s algorithm for computing gcd(m, n) for 1≤...

Sample Execution : Recursive Euclidean Algorithm to calculate GCD Type a positive integer for...

Use the Euclidean algorithm to find the GCD of 3 + 9i and 7-i

a. Using the Euclidean Algorithm and Extended Euclidean Algorithm, show that gcd(99; 5) = 1 and...

1. Calculate gcd(181451, 186623). 2. For integers a, b, and c, if a | bc, then...

Write an algorithm to input a number n, then calculate 13 +2 3 + 33 +...