Exercise 1. Show that the only automorphism of Q(³√2) is the identity.
Exercise 2. Show that if z∈C is a root of f(x)∈R[x], then ̅z is also a root of f(x).
Exercise 3. If p is a prime and n∈Z+, show that xⁿ¯p is irreducible over Q.
Exercise 6. If p is a prime, show that 1 +x +x² +...+xᵖ¯¹ is irreducible over Q.
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