1. The number of integer pairs $(x, y)$ that satisfy $x^{2}-4 y^{2}=2011$ is ( ).
(A) 0
(B) 1
(C) 2
(D) 3
-1.A.
If the integer pair $(x, y)$ satisfies
$$
x^{2}-4 y^{2}=2011 \text{, }
$$

but the left side $x^{2}-4 y^{2}$ when divided by 4 leaves a remainder of 1 or 0, while the right side 2011 when divided by 4 leaves a remainder of 3, which is a contradiction.