12. Given that $a$ and $b$ are integers. If $a^{2}-b^{2}=2003$, then the value of $a^{2}+b^{2}$ is ( ).
(A) 2006005
(B) 2005004
(C) 2004003
(D) 2003002
(E) 2002001
12.A.

An intuitive method is that it is easy to see the last digit of $a^{2}+b^{2}$ can only be 5, therefore, it can only be $(\mathrm{A})$.