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Topic: rewriting my earlier proof of FLT: please critique
Replies: 10   Last Post: Jan 19, 2014 4:19 PM

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Brian Q. Hutchings

Posts: 5,649
Registered: 12/6/04
Re: rewriting my earlier proof of FLT: please critique
Posted: Jan 18, 2014 3:37 PM
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how, so, p | c+d ??

> B. c^n + d^n > p^n .... (13)
>
> so p divides c+d, let us write c + d = Mp.
>
> adding (5) and (6) gives us, a + b = p^n (j+k) + Mp ...... (14)
>
> Implies p divides a+b, which violates our assumption (5)
>
> This logic will work even if we assume a = jp^n +/- c and b = kp^n +- d
>
>
>
> C. c^n + d^n = 0 possible when c and d are both zero (violates (9))
>
> or c = -d and adding (7) and (8) will give us a+b = p^n (j+k)
>
> and so p divides a+b, which violates our assumption (5)
>
>
>
> D. Let us assume p divides(both a+b) and Q.
>
> We know that the only number that divides a+b and Q is n.
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>
>
> C. Q = n (so n^(n-1) divides a+b)
>
> Q = a^(n-1) b + a^(n-2)b^2 + .... + b^(n-1)
>
> Q = n possible if both a and b are equal to 1.
>
>
>
> D. Q = n^(n-1) [and n divides a+b]
>
> then n divides a or b and hence n divides d in (2), violates (1)
>
>
>
> C. Q has a factor q (not equal to n) that is not a factor of (a+b).
>
> This is not possible as shown in (12), (13) and (14)
>
>
>
> I think this rounds out the proof.





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