ok so it is just a special case, so if p | a^n then the fact that p should divide one of the a_i means simply p|a, since every a_i is a.
so from p |a^n implies p |a .
so if p divides a we have that p(q) = a for some integer q.
since we have an equation, i can raise both sides to the n...
The question states prove,
If p is prime and p | a^n then p^n | a^n
I am pretty sure I have i just may need someone to help clean it up.
There are two relevant theorems i have for this.
the first says p is prime if and if p has the property that if p | ab then p | a or p | b
the...