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| + | First notice <math>(x-c^\frac{1}{p})^p = x^p-c </math>. | ||
| − | + | So <math> F(c^\frac{1}{p})</math> is the splitting field of <math> x^p-c </math>. | |
| + | |||
| + | Now suppose that the polynomial is reducible in some field K. | ||
Revision as of 04:20, 3 July 2013
NinjaSharkSet5Problem1
First notice $ (x-c^\frac{1}{p})^p = x^p-c $.
So $ F(c^\frac{1}{p}) $ is the splitting field of $ x^p-c $.
Now suppose that the polynomial is reducible in some field K.
