Using the Extended Euclidean Algorithm, find the multiplicative inverse of:
31 mod 3480
Using the Extended Euclidean Algorithm, find the multiplicative inverse of: 31 mod 3480
Please solve the above 4 questions. 1. Using the extended Euclidean Algorithm, find all solutions of the linear congruence 217x 133 (mod 329), where 0 x < 329 (Eg. if 5n, n 0,. ,6) 24 + 5n, п %3D 0, 1, . .., 6, type 24 + x< 11 2. Find all solutions of the congruence 7x = 5 (mod 11) where 0 (Eg. if 4,7 10, 13, type 4,7,10,13, none. or if there are no solutions, type I 3....
1125 and b 56 (a) Find ged(a, b) using: (i) The Euclidean Algorithm (ii) The fundamental Theorem of Arithmetic. (b) Use the Euclidean Algorithm to find: (i) x and y such that ax by ged(a, b) (ii) The multiplicative inverse of 56 in the group Z25. Let a =
1. (a) Use the Extended Euclidean Algorithmn to compute the inverse of 10 mod 17. (b) Use your answer from (a) so solve the equation 10x = 8 mod 17. (c) Compute 1616 mod 17. You may assume that Fermat’s Little Theorem is true.
20 points Problem 4: Extended Euclidean Algorithm Using Extended Euclidean Algorithm compute the greatest common divisor and Bézout's coefficients for the pairs of integer numbers a and b below. Express the greatest common divisor as a linear combination with integer coefficients) of a and b. (Do not use factorizations or inspection. Please demonstrate all steps of the Extended Euclidean Algo- rithm.) (a) a 270 and b = 219 (b) a 869 and b 605 (c) a 4930 and b-1292 (d)...
Describe the extended Euclidean algorithm for two positive integers. Simulate the extended Euclidean algorithm for two particular positive integers.
Please answer the question below: use this as an example follow the same steps please! thanks 3. (10 points) Find the modular multiplicative inverse of 14 mod 33 using the Extended Eu- clidean Algorithm. Example 3. Find the multiplicative inverse of 8 mod 11, using the Euclidean Algorithm Solution. We'l organize our work carefully. We'll do the Euclidean Algorithm in the left column. It will verify that god(8,11) = 1. Then we'll solve for the renainders in the right column,...
A. Find the multiplicative inverse of 52 mod 77. Your answer should be an integer s in the range from 0 through 76. Check your solution by verifying that 52s mod n = 1. Show that for all integers a, b, and c, if aſb and alc, then a-|bc.
Using the Euclidean Algorithm show that gcd (193, 977) Now find integers s, t such that 193s +977t-1, and use this to find the value of a that satisfies the congruence 193a 38 (mod 977) Using the Euclidean Algorithm show that gcd (193, 977) Now find integers s, t such that 193s +977t-1, and use this to find the value of a that satisfies the congruence 193a 38 (mod 977)
6. Using the Euclidean Algorithm show that gcd (109, 736) 1 Now find integers s, t such that 109s + 736t 1, and use this to find the value of r that satisfies the congruence 109x 71 (mod 736). 6. Using the Euclidean Algorithm show that gcd (109, 736) 1 Now find integers s, t such that 109s + 736t 1, and use this to find the value of r that satisfies the congruence 109x 71 (mod 736).
If n = 456917 and p and q are its two factors, find the multiplicative inverse of 101 mod n-p-q.