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.

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Chapter2: Second-order Linear Odes
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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,)* ?)
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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