Let n = pq be the product of two odd primes. Recall that there are no primitive roots modulo n. Show that there are in fact 3 incongruent values of a such that ordn(a) = 2. Using this in combination with part (a), present an alternate proof that there are no primitive roots modulo pq. Where does this proof break down if p = 2? (Hint: Chinese Remainder Theorem.)

Let n = pq be the product of two odd primes. Recall that there are no primitive roots modulo n. Show that there are in fact 3 incongruent values of a such that ordn(a) = 2. Using this in combination with part (a), present an alternate proof that there are no primitive roots modulo pq. Where does this proof break down if p = 2? (Hint: Chinese Remainder Theorem.)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.5: Congruence Of Integers

Problem 34E

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