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I can prove part a if p is prime, but I'm not sure how to prove that p is prime.  Any ideas?
 
I can prove part a if p is prime, but I'm not sure how to prove that p is prime.  Any ideas?
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Let X = x^(p^(n-1))
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Let Y = y^(p^(n-1))
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From part a & induction:
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(X+Y)^p = X^p + Y^p = x^p^n + y^p^n
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and
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(X+Y)^p = (x^(p^(n-1))+y^(p^(n-1)))^p = (x+y)^p^n = x^p^n + y^p^n.

Revision as of 17:51, 26 October 2008

  • I am kinda lost in this chapter. Could someone enlighten me on this question? I missed one of the lecture.

-Wooi-Chen Ng

I can prove part a if p is prime, but I'm not sure how to prove that p is prime. Any ideas?


Let X = x^(p^(n-1)) Let Y = y^(p^(n-1))

From part a & induction:

(X+Y)^p = X^p + Y^p = x^p^n + y^p^n

and

(X+Y)^p = (x^(p^(n-1))+y^(p^(n-1)))^p = (x+y)^p^n = x^p^n + y^p^n.

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