Re: Solving a 3D systems of equations


fred botjon wrote:
"Randy Poe" <poespam-trap@xxxxxxxxx> wrote in message
news:1156880936.178409.317800@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Obviously not. The equation x + y + z = w means that
x is at most w/3.

wrong.

An even simpler counterargument. Given x<y<z and x+y+z = w.

Since y>x, z>z, then x+y+z > x + x + x = 3x. So w > 3x. x is
at most w/3. This is true even if you don't restrict to natural
numbers.

The equation xyz = a means x is at most
cuberoot(a).

wrong.

x<y<z so xyz > x*x*x, i.e. a > x^3. Therefore x < cuberoot(a).
Again, this is true even without the restriction to natural numbers.

So there are finitely many possible values for x,
and similarly for y and z.

wrong.

This is of course true only when you add the restriction to natural
numbers, which OP did.

- Randy

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