Let $q=p^n$, $p$ prime, ¿Which $q$ satisfies $\mathbb{F}_{q^2}=\mathbb{F}_q(\sqrt{a})$?. I don't know why is necessary a condition for $q$.
Let $q=p^n$, $p$ prime, ¿Which $q$ satisfies $\mathbb{F}_{q^2}=\mathbb{F}_q(\sqrt{a})$?.
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field-theory
galois-theory
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1See the a$n$swer to [this related questio$n$](http://math.stackexcha$n$ge.com/q/204245/15941) for ideas – 2012-09-30
1 Answers
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Hint: If $p\ne 2$, any polynomial $x^2+ax+b$ can be written in the form...