Date: Dec 31, 2012 1:42 AM
Author: John Jens
Subject: Re: From Fermat little theorem to Fermat Last Theorem
On Sunday, December 30, 2012 9:51:08 PM UTC+2, quasi wrote:

> John Jens wrote:

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> >I pick a < p ,proved that do not exist a , b , c

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> >rational numbers with 0<a=<b<c and a<p to satisfy

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> >a^p+b^p=c^p

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> No, you never proved the above claim.

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>

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> You only thought you did.

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> First you tried to show that the equation

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>

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> a^p + b^p = c^p

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>

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> has no solutions in integers a,b,c,p subject to the

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> conditions 0 < a <= b < c, p > 2, a < p.

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> For the sake of argument, let's allow that claim.

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> Then you attempted to extend to positive rationals a,b,c. To do

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> that, you scale a,b,c down, dividing each by a positive integer

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> large enough so the new value of a is less than p. Then you

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> claim a contradiction since you already showed that a < p is

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> impossible. But you showed that for positive integer values of

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> a, not for positive rational values of a, so (barring circular

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> reasoning) you don't have your claimed contradiction.

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>

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> quasi

I intentionally choose a < p ,there's no crime to choose

an a natural, a < p.

If for a < p ,a,b,c, naturals , we can multiply the inequality a^p + b^p != c^p with any rational number,

it will remain a inequality.