My Math Forum Proof Regarding Primes to a Power

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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 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 234 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 $p | a \ \$then for some integer c , $\ \ a \= \ cp$ $a^n \= \ (cp)^n \ \ \Right \ \ a^n \ = \ c^np^n \ \ \Right \ \ p^n | (c^np^n) \ \ \Right \ \ p^n | a^n$

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