Let \(F\) be a finite field, and suppose that the subfield of \(F\) generated by \(\{x^3\mid x\in F\}\) is different from \(F\). Show that the cardinality of \(F\) is 4.
Question
Math 6310 • Algebra
Fall 2004 • Question 7
Question
Fall 2004 • Question 7
Let \(F\) be a finite field, and suppose that the subfield of \(F\) generated by \(\{x^3\mid x\in F\}\) is different from \(F\). Show that the cardinality of \(F\) is 4.