p=317, q=811 (a) Consider the multiplicative group F∗p and find a generator (primitive root) of it. Hint: F∗p has ϕ(p) = p − 1 elements and the order of an element must divide the order of group. (b) Use the extended Euclidean Algorithm to compute the inverse of 5 mod p.

p=317, q=811 (a) Consider the multiplicative group F∗p and find a generator (primitive root) of it. Hint: F∗p has ϕ(p) = p − 1 elements and the order of an element must divide the order of group. (b) Use the extended Euclidean Algorithm to compute the inverse of 5 mod p.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.8: Some Results On Finite Abelian Groups (optional)

Problem 15E: 15. Assume that can be written as the direct sum , where is a cyclic group of order . Prove that...

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