show no solutions exists using table x^3mod9

Hi wondering if anyone can help with this question:

Make a table of values x^3, mod 9, and show that the equation x^2 + 2y^2 = 9z^2 has no non zero integer solutions.

My table looks like

n mod 9 - -4 -3 -2 -1 0 1 2 3 4

n^3mod 9 - -1 0 1 -1 0 1 -1 0 1

2n^3mod 9 --2 0 2 -2 0 2 -2 0 2

i can see that by adding the two rows i get 0's at 0 and +-3 but dont really know where to go from here.

Also if i am not given the modulo to use, how do i decide which modulo to use.

Thanks in advance

Re: show no solutions exists using table x^3mod9

Re: show no solutions exists using table x^3mod9

You'll want to make a table for mod 9. For example,

Assume that at least one of x,y,z is not a multiple of 3. Even then, you can't prove that using the table, for example, you could have