MathNet 2011 Question 59

Positive integers x and y satisfy that $x^2-y^2$ is positive, divisible by 2011, and has exactly 2011 positive divisors. How many ordered pairs (x,y) satisfy these conditions? Note: 2011 is prime.
(A) 2010; (B) 2011; (C) 1005; (D) 0; (E) Infinitely many.