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Problem 4. Let K be a field and let f ∈ K[x]. Show that if 1+f2...

Problem 4. Let K be a field and let f ∈ K[x]. Show that if 1+f2 has a factor of odd degree in K[x] then there is an a ∈ K such that a2 = −1.

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Soln Assume that . 11.42 ha, a .facto. . ca odal-de Reun KCg_ Toshouo--4herme ts an aek Such that a- -t 15 2n+1 r Some . 2 25

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