Question 67
Find the least positive integer $a$ such that the system
$$
\left\lvert\, \begin{aligned}
& x+y+z=a \\
& x^{3}+y^{3}+z^{2}=a
\end{aligned}\right.
$$
has no integer solution.
$$
\left\lvert\, \begin{aligned}
& x+y+z=a \\
& x^{3}+y^{3}+z^{2}=a
\end{aligned}\right.
$$
has no integer solution.