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Calculus and Beyond Homework Help
Given that p is a prime? (Review/verify this proof)?
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[QUOTE="Math100, post: 6607160, member: 639945"] [B]Homework Statement:[/B] Given that ##p## is a prime and ##p\mid a^n ##, prove that ## p^n \mid a^n ##. [B]Relevant Equations:[/B] None. Proof: Suppose that p is a prime and ##p \mid a^n ##. Note that a prime number is a number that has only two factors, 1 and the number itself. Then we have (p*1)##\mid##a*## a^{(n-1)} ##. Thus p##\mid##a, which implies that pk=a for some k##\in\mathbb{Z}##. Now we have ## a^n ##=## (pk)^n ## =## p^n k^n ##. This means ##p^n \mid a^n ##. Therefore, given that p is a prime and ##p \mid a^n ##, we have proven that ##p^n \mid a^n ##. [/QUOTE]
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Calculus and Beyond Homework Help
Given that p is a prime? (Review/verify this proof)?
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