MathNet 2007-part-02 — 187 problems (EN–VI) Question 68

A positive integer is called triangular if it can be written in the form $\frac{n(n+1)}{2}$ for some positive integer $n$. How many pairs $(a, b)$ of triangular numbers are there such that $b-a=2007$? (Recall that 223 is a prime number.)