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kentonyee@xxxxxxxxxxx wrote:
> I'm dissapointed that the solutions are not more interesting. Would
> they become more interesting if, instead, the condition is
> V(x,y,z) + V(a,c,d) = V(x + V(a,c,d), y + c, z + d)
> for ALL x,y,z,a,c,d?
Unfortunately not really. On both the planes (x,y,0) and (x,0,z) we
have the same relations as before, leading to the same solutions in
that plane.
If V(x,0,0) = x, then V(x,y,z) = x is the only solution.
If V(x,0,0) = 0, then the original solution yields V(x,y,0) = A y and
V(x,0,z) = B z. A little more manipulation reveals that the only
solutions are of the form V(x,y,z) = A y + B z.
- Tim
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