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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)) | ||
| + | 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.
