Re: x^2 + y^2 + z^2 = r^2 + s^2 + t^2


"Pavel Pokorny" <Pavel.Pokorny@xxxxxxxxxxxxxxxxxxxxxxx> wrote in message
news:d2rsbe$24nq$1@xxxxxxxxxxxxxxxxxx
>
> Dear math friends
>
> can you, please, tell me how to solve
>
> x + y + z = r + s + t
> x^2 + y^2 + z^2 = r^2 + s^2 + t^2
>
> for integer numbers?
> Has this problem its name?
> Is it related to Fourier transform?
>
> P.S.
> This is not a homework, on the contrary:
> one of my students has asked me.

OK! Hint. x+y+z always divides x^n+y^n +z^n as x,y,z and n are integers >0.
There are integers x,y,z >0 so that x+y+z divides always x^n+y^n +z^n for
any integer n >0.
Use google in sci.math. The solution is parametric. ;-)

Tapio
>
> --
> Pavel Pokorny
> Math Dept, Prague Institute of Chemical Technology
> http://www.vscht.cz/mat/Pavel.Pokorny


.

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