Suppose g is a primitive root mod p (with p an odd prime) such that g^p-1 =/ 1 mod p+ Prove g must be a primitive root mod p^2 Use this to prove 2 is a primitive root mod 25 Then find all the primitive roots mod 25 (briefly explain)

Suppose g is a primitive root mod p (with p an odd prime) such that g^p-1 =/ 1 mod p+ Prove g must be a primitive root mod p^2 Use this to prove 2 is a primitive root mod 25 Then find all the primitive roots mod 25 (briefly explain)

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 30E: 30. Prove that any positive integer is congruent to its units digit modulo .

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Question

Suppose g is a primitive root mod p (with p an odd prime) such that g^p-1 =/ 1 mod p+ Prove g must be a primitive root mod p^2
Use this to prove 2 is a primitive root mod 25
Then find all the primitive roots mod 25 (briefly explain)

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