Last problem I had from my exam:

Let be an extension field of a field whose char is . Let be an element of which is separable over and for which there exists a positive integer such that . Show that .

The first thing that bugged me was that it wasn't clear if or had char , but then it seems that whichever has char means that the other would also have char . I'm also tempted to assume that is prime, but that would be presumptuous of me

I'm not sure what to do. Any help would be much appreciated