--- --- --- Solutions of an equation

Assertion:

The following equation (1) cannot be satisfied if all of x, y, z are
integers each > 1.

x^2 + 8y^2 = z^2 (1)

My approach: x, (sqrt (8)y), z represent the three sides of a
Pythegorian triangle. Given y is an integer sqrt(8)y can never be an
integer. Therefore, it can be argued that (1) has no integer
solutions.

Any helpful comments will be appreciated.
.