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Topic: (u-1)^n = u^n -1 (mod n^3) more than two solutions?
Replies: 24   Last Post: Jul 15, 2014 2:04 AM

 Messages: [ Previous | Next ]
 robersi Posts: 2,410 From: NNY Registered: 8/18/09
Re: (u-1)^n = u^n -1 (mod n^3) more than two solutions?
Posted: Jul 14, 2014 10:38 PM

On Monday, July 14, 2014 10:22:38 PM UTC-4, rober...@gmail.com wrote:
> On Monday, July 14, 2014 9:35:04 PM UTC-4, quasi wrote:
>

> > quasi wrote:
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> >
>
> > >robersi730 wrote:
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> >
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> > >>quasi wrote:
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> >
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> > >>>robersi730 wrote:
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> >
>
> > >>>>
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> >
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> > >>>>Let there be a non zero integer solution to a^n+b^n=c^n
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> >
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> > >>>>where n is an odd prime.
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> >
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> > >>>>
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> >
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> > >>>>Also let a,b,c be such that none is divisible by n.
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> >
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> > >>>
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> >
>
> > >>>Ok so far (for case 1 of FLT)
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> >
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> > >>>
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> >
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> > >>>>And let a+b=c (mod n^2)
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> >
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> > >>>
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> >
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> > >>>That's a pretty strong assumption.
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> >
>
> > >>>
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> >
>
> > >>>By Fermat's little Theorem, it's automatic that
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> >
>
> > >>>
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> >
>
> > >>> a + b = c (mod n)
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> >
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> > >>>
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> >
>
> > >>>but I don't see how to prove
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> >
>
> > >>>
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> >
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> > >>> a + b = c (mod n^2)
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> >
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> > >>>
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> >
>
> > >>>Can you prove the above from the prior hypotheses?
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> >
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> > >>>
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> >
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> > >>>If not, any contradiction you might get would only prove
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> >
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> > >>>that a hypothetical nontrivial solution a,b,c would have
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> >
>
> > >>>to be such that a + b != c (mod n^2).
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> >
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> > >>
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> >
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> > >>Yea actually I can prove
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> >
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> > >>
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> >
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> > >> a^n = a mod n^2
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> >
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> > >> b^n = b mod n^2
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> >
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> > >> c^n = c mod n^2
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> >
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> > >
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> >
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> > >Sorry, I looked at the pdf of your claimed proof.
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> >
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> > >
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> >
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> > >The proof has fatal flaws.
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> >
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> >
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> >
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> > Parts of your proof are correct, so there may actually be
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> >
>
> > a non-trivial result that can be salvaged from that mess.
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> >
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> >
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> >
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> > If I have time, I'll try to post a readable version of what
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> >
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> > I think your work actually shows.
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> >
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> >
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> >
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> > quasi
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>
>
> What do you think it actually shows?

nevermind

>
>
>
> What are the flaws?
>

nevermind
>
>
> If you can write it better be my guest.
>

I'll be second author
>
>
> Mess? yes Sound? YES!

nevermind

Simon

Date Subject Author
7/12/14 robersi
7/12/14 Brian Q. Hutchings
7/12/14 robersi
7/12/14 quasi
7/12/14 robersi
7/14/14 robersi
7/14/14 quasi
7/14/14 robersi
7/14/14 quasi
7/14/14 quasi
7/14/14 robersi
7/14/14 robersi
7/14/14 quasi
7/14/14 quasi
7/14/14 robersi
7/14/14 quasi
7/15/14 robersi
7/15/14 quasi
7/15/14 robersi
7/15/14 quasi
7/15/14 quasi
7/13/14 quasi
7/14/14 Timothy Murphy
7/14/14 James Waldby
7/13/14 robersi