2. Find all values of the parameter $a$ for which the equation $2 x^{2}-a x+2 a=0$ has two distinct integer roots.
2.II.2. Setting $a=2b$, we get the equation $x^{2}-b x+2 b=0$. If $m$ and $n$ are its integer roots, then $m n=2 b$ and $m+n=b$, so $m n=2 m+2 n$, or $(m-2)(n-2)=4$, from which

$$
(m ; n)=(0 ; 0),(4 ; 4),(6 ; 3),(3 ; 6),(1 ;-2),(-2 ; 1)
$$

Thus, $b$ can take one of the values $0 ;-1 ; 8 ; 9$. Checking shows that the equation has two distinct integer roots when $b=-1$ and $b=9$.

Answer: $-2 ; 18$.