<s>[INST] Integer solutions of $ x^3+y^3+z^3=(x+y+z)^3 $ Consider the equation
$$ x^3+y^3+z^3=(x+y+z)^3 $$
for triples of integers $(x, y, z) $.
I noticed that this has infinitely many solutions: $ x, y $ arbitrary and $ z=-y $. 
Are there more solutions?
 [/INST] For such equations :
$$(x+y)^3+x^3+y^3+z^3=(x+y+z)^3$$
You can write the formula.
$$x=3p^2+18ps-s^2$$
$$y=15p^2-6ps-5s^2$$
$$z=3p^2-6ps+7s^2$$
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