Problem 2. Consider the abelian group Z/nZ under addition. Define a binary operation [a] * [b] := [a · 6] - 8) Prove that forpa prime, (F,)" is a cyclic group of order p - 1.
Problem 2. Consider the abelian group Z/nZ under addition. Define a binary operation [a] * [b] := [a · 6] - 8) Prove that forpa prime, (F,)" is a cyclic group of order p - 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. g
![Problem 2. Consider the abelian group Z/nZ under addition. Define a binary operation
[a] * [6] := [a - 6) .
g) Prove that for pa prime, (F,)" is a cyclic group of order p– 1.
h) Prove Fermat's Little Theorem: Let p be any prime and a any integer. Then a" is
equivalent to a modulo p. (Hint: What is the order of the group (F,)* ?)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39e7c5be-e61c-44aa-a62c-e34cd504af8d%2Fd1bf14c7-150b-402b-937b-9d64dcaf373d%2Fb4wlcgo_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 2. Consider the abelian group Z/nZ under addition. Define a binary operation
[a] * [6] := [a - 6) .
g) Prove that for pa prime, (F,)" is a cyclic group of order p– 1.
h) Prove Fermat's Little Theorem: Let p be any prime and a any integer. Then a" is
equivalent to a modulo p. (Hint: What is the order of the group (F,)* ?)
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