First, we obviously have the trivial solution

Now suppose there's another solution

If and are not multiples of 3 then a contradiction.

Again ifonlyone of them ( x or z) is multiple of 3 we get a contradiction ( try it).

So both, and are multiples of 3. And thus is multiple of 9, so it must be that is multiple of 3. Now set ; ;

We get: (dividing by 9)

And it follows by infinite descent that there can be no other solution.