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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Summer 2017 • Question 7

Question

Math 6310 • Algebra Summer 2017 • Question 7

Let \(p\) be a prime number and \(n\) a positive integer. How many elements \(\alpha \) are in \(\mathbb {F}_{p^n}\) such that \(\mathbb {F}_p(\alpha )=\mathbb {F}_{p^6}\)?

Raw LaTeX

Let \(p\) be a prime number and \(n\) a positive integer. How many elements \(\alpha\) are in
\(\mathbb{F}_{p^n}\) such that \(\mathbb{F}_p(\alpha)=\mathbb{F}_{p^6}\)?

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Finite Fields