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        riddles >> medium >> Proof (?) of Fermat's Last Theorem
        
(Message started by: cool_joh on Dec 19th, 2007, 7:39pm)
Title: Proof (?) of Fermat's Last Theorem
Post by cool_joh on Dec 19th, 2007, 7:39pm
an+bn=cn
an-0n=cn-bn

n=3, sequence of power: 0, 1, 8, 27, 64, 125
n=4, seq: 0, 1, 16, 81, 256...
and so on.

Note that the difference goes larger as the sequence goes higher. So it's impossible that there are two pairs of terms which has the same differences.

Sorry about my poor English, I hope you understand.

But, I doubt that this really prove the theorem. Can anyone find any mistakes?

---inspired by nick (http://www.qbyte.org/puzzles/p061s.html)
Title: Re: Proof (?) of Fermat's Last Theorem
Post by Obob on Dec 19th, 2007, 9:33pm
The logic just plain doesn't work, is what the error is.  By the exact same argument, a2+b2=c2 shouldn't have any solutions either, which is absurd.

There is no obvious reason why the difference of two terms in the n=4 sequence shouldn't again be in the n=4 sequence, for instance.
Title: Re: Proof (?) of Fermat's Last Theorem
Post by Hippo on Dec 20th, 2007, 4:17am

on 12/19/07 at 19:39:36, cool_joh wrote:
an+bn=cn
an-0n=cn-bn

n=3, sequence of power: 0, 1, 8, 27, 64, 125
n=4, seq: 0, 1, 16, 81, 256...
and so on.

Note that the difference goes larger as the sequence goes higher. So it's impossible that there are two pairs of terms which has the same differences.

Sorry about my poor English, I hope you understand.

But, I doubt that this really prove the theorem. Can anyone find any mistakes?

---inspired by nick (http://www.qbyte.org/puzzles/p061s.html)


Noone talks about differences of neighbouring members. ...
Title: Re: Proof (?) of Fermat's Last Theorem
Post by SMQ on Dec 20th, 2007, 5:42am

on 12/19/07 at 19:39:36, cool_joh wrote:
Note that the difference goes larger as the sequence goes higher. So it's impossible that there are two pairs of terms which has the same differences.

But that's just as true of the sequence of squares: 0, 1, 4, 9, 16, 25, ...  yet 9 + 16 = 25 (and those are even adjacent terms!).

--SMQ
Title: Re: Proof (?) of Fermat's Last Theorem
Post by Grimbal on Dec 20th, 2007, 6:35am
It also happens that  123-93 = 103-13
Title: Re: Proof (?) of Fermat's Last Theorem
Post by FiBsTeR on Dec 20th, 2007, 5:11pm

on 12/20/07 at 06:35:33, Grimbal wrote:
It also happens that  123-93 = 103-13


Dr. Taxicab (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_easy;action=display;num=1194039906) would be proud.   :'(


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