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

Quote:

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Originally Posted by MattWT

Hi wondering if anyone can help with this question:

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 ?

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	0	1	2	3	4	5	6	7	8
	0	1	8	0	1	8	0	1	8

btw, are you sure you're not being asked to construct table for not ?

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