Integer equation 
Author Message
 Integer equation
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



Sun, 09 Aug 2009 12:55:55 GMT
 Integer equation

Quote:
> Dear all

to make it a bit easer I will remove some restrictions as explained below
Quote:

> 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 distinct coprime
> integers belonging to Z,
> then the following integer equation doesn't have any
> solution  in the whole Integer number system as defined above

>           n^3 = m^3 + k^3 + 2*n*m*k

> Thanking you a lot

> Bassam King Karzeddin
> Al-Hussein Bin Talal University
> JORDAN

> Message was edited by: bassam king karzeddin



Sun, 09 Aug 2009 15:49:43 GMT
 Integer equation
In article


Quote:
> 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

There is some discussion of this equation in Mordell, Diophantine
Equations, especially starting on page 78 and starting on page 130.

--



Mon, 10 Aug 2009 08:01:20 GMT
 
 [ 3 post ] 

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