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February 8th, 2014, 04:48 PM   #1
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Proof Regarding Primes to a Power

So I have the question: http://i.imgur.com/IUAaM90.png

I know that if p|a^n then p|a(a)(a)...(a) n times and therefore p|a.

I'm having some trouble finding a property that can either prove or disprove that p^n|a^n assuming p|a^n. Could someone point me in the right direction? Thank you so much.
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February 8th, 2014, 10:08 PM   #2
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Re: Proof Regarding Primes to a Power

Well , you are very close to proving it , use your result p|a , you just need one more truth.

Since

then for some integer c ,



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