Fwd: Diophantine equation with factorial

[Richard Guy]

Where angels fear to tread ?

x^3 + y^3 = (x + y)(x^2 - xy + y^2)   and all squarefree
factors of the latter paren are  3  or of form  6k + 1.  R.

On Sun, 22 Jun 2003 all at abouthugo.de wrote:

> 
> SeqFans,
> 
> a few days ago the following was posted to
> NG sci.math.research. No reply so far.
> At least there don't seem too many solutions....
> Any ideas?
> 
> Hugo 
> > 
> > -------- Original Message --------
> > Betreff: Diophantine equation with factorial
> > Datum: Thu, 19 Jun 2003 15:26:48 GMT
> > Von: Alex Liu <mrlwk at netvigator.com>
> > Foren: sci.math.research
> > 
> > It is clear that (x,y,n)=(1,1,2) is [a] positive integer solution to
> > the equation x^3+y^3=(n!). Any other positive integer solution to this
> > equation?
>