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Topic: Re: Integer equation
Replies: 2   Last Post: Oct 31, 2017 2:28 PM

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bassam king karzeddin

Posts: 1,260
Registered: 12/8/04
Re: Integer equation
Posted: Oct 18, 2017 10:00 AM
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> On Wednesday, 21 February 2007 09:55:55 UTC,
> karzeddin wrote:

> > Dear all
> >
> > I would like to know a counter example to the

> following integer equation where I think there is no
> one at all, hoping to be mistaken

> >
> > PUZZLE
> >
> > IF (n, m, k) are three positive distinct coprime

> integers ,where (m, k) are odd integers,
> >
> > then the following integer equation doesn't have

> any solution in the whole number system as defind
> above

> >
> > n^3 = m^3 + k^3 + 2*n*m*k
> >
> > Thanking you a lot
> >
> > Bassam King Karzeddin
> > Al-Hussein Bin Talal University
> > JORDAN

>
> This is the 'coordinate equation' in Unity Root
> Matrix Theory (URMT) for the specific '2' case
> (unfortunately there is a clash in my notation in
> URMT where 'k' = 2, i.e. 2*n*m*k and not the 'k' you
> use above.
>
> Apart from extensive theoretical analysis of this
> equation in URMT, there is some numerical analysis of
> the more general problem in the relatively recent
> document
>
> http://www.urmt.org/urmt_numeric_solutions.pdf
>
> I note G. Myerson posts some discussion on the
> specific case '2', and it would be nice if Gerry
> expands upon the results in his quoted text
> 'Mordell'.
>
> For the 3*n*m*k solution, n=m+k is the simple
> solution for '3', i.e. 3*n*m*k, also in my above
> quoted text, but I would like to know about a '2'
> solution if any?
>
>
> Richard Miller
> http://www.urmt.org


Your paper seems useful and interesting, I will study it once I get time, since it is Diophantine Eqns. and I don't know what did G.Myrsone meant exactly by his meaningless comment since I don't have any axis to any Journal, so he was just unclear and most likely his comment is useless regarding this issue

Probably he wanted to say that someone before had talked about this problem, (that is all), where he didn't mention whether it was at least conjectured or proved or anything else, just to kill the whole issue for a purpose he knows much better

At any case, the conjecture is true and a theorem for (at least my self), since I had proved it to my self first and long time ago, but frankly not bothering to throw it to mainstream mathematicians because certainly, they would teach me my own proof most likely on the second day, adding that I'm not any professional researcher to write it the way they require

So, let them enjoy it at least for a century, and truly speaking this problem is too easy for me, where I had PUBLISHED here much more difficult ones

Regards
Bassam King Karzeddin
Oct. 18, 2017



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