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From: TPiezas on 20 Apr 2010 05:06
On Apr 19, 11:22 am, Robert Israel
<isr...(a)math.MyUniversitysInitials.ca> wrote:
> TPiezas <tpie...(a)gmail.com> writes:
> > Hello all,
>
> > The classical result that any non-zero rational constant is the sum of
> > 3 rational 3rd powers in an _infinite_ number of ways can be shown
> > true by the new Ellison's Identity.
>
> > This involves only a 3rd deg polynomial in the constant (in contrast
> > to Ryley's Identity which was a 6th-deg), with simple coefficients
> > that are only powers of 3.
>
> >http://sites.google.com/site/tpiezas/updates04
>
> You don't need such big powers of 3 either.  Ellison's Identity can be written as
>
> (27 m^3 - t^9)^3 + (-27 m^3 + 9 m t^6 + t^9)^3 + (27 m^2 t^3 + 9 m t^6)^3
>    = m (27 m^2 t^2 + 9 m t^5 + 3 t^8)^3
>
> (corresponding to t = 3 n)
> --
> Robert Israel              isr...(a)math.MyUniversitysInitials.ca
> Department of Mathematics        http://www.math.ubc.ca/~israel
> University of British Columbia            Vancouver, BC, Canada


Thanks. Update has been modified.

(Prof. Ellison replied that he only found the identity in a book.
From his first email, I thought it was his. Anyway, that detail has
been changed also.)

- Titus
From: master1729 on 20 Apr 2010 03:02
> first , i wonder why you all write = N
>
> and not = Q.
>
> however the link is clear , so the title is in some
> sense correct afterall.
>
> inspired by Euler ( sum of powers conjecture ) and
> Fermat ( FLT and Polygonal Number theorem ) , i
> wonder about the following :
>
> -- though i seem to remind that this was already
> settled and classical , my memory = bad ? --
>
> for n >=3
> any non-zero rational constant is the sum of n
> rational nth powers.
>
> i guess a big difference for n = even , since then
> only + can occur.
>
> maybe n = prime is an intresting special case.
>
> i feel ive seen this before ...
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