814. Does the equation

$$
x^{3}+y^{3}=9 z+5
$$

have solutions in integers $x, y$ and $z ?$
$\triangle$ The cube of an integer, when divided by 9, can only leave a remainder of 0, 1, or 8 (we have already encountered this in solving some problems in § 8). Consequently, the sum of two perfect cubes, when divided by 9, cannot leave a remainder of 5. In other words, the given equation does not hold for any integer values of $x, y$, and $z$.

Answer: does not have.