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The sum of all positive integers for which the quotient and remainder are equal if the number is divided by 2008 is __________
Correct Answer: 4048191252
Such a number is $$n = 2008r + r = 2009r$$, where the remainder $$r$$ must satisfy $$1 \le r \le 2007$$ for $$n$$ to be positive. The sum is $$2009(1 + 2 + \cdots + 2007) = 2009 \times \frac{2007 \times 2008}{2} = 2009 \times 2015028 = 4048191252$$.
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