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1. The problem statement, all variables and given/known data

Let [itex]\bar{\mathbb{Z}}_p[/itex] be the algebraic closure of [itex]\mathbb{Z}_p[/itex] and let K be the subset of [itex]\bar{\mathbb{Z}}_p[/itex] consisting of all of the zeros of [itex]x^{p^n} - x[/itex] in [itex]\bar{\mathbb{Z}}_p[/itex]. My book proved that the subset K is actually a subfield of [itex]\bar{\mathbb{Z}}_p[/itex] and that it contains p^n elements. Then, out of nowhere, it said that K contains Z_p and provided absolutely no justification for that claim. Can someone fill me in on why that is so obvious?

2. Relevant equations

3. The attempt at a solution

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# Galois fields

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