$(0,0,0)$ is a solution From (2) $b \mid c$ From (3) $b \mid a$ From (2) $b^3 \mid abc \Rightarrow b^3 \mid c$ From (2) $c \mid b^3 \Rightarrow c=\pm b^3$ From (2) $2=ab \Rightarrow$ $b=1,a=2$ or $b=-1,a=-2$ Solutions: $(a,b,c)=(0,0,0);(2,1,1);(-2,-1,-1)$