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categories: Mathematics
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Sums of the form $$\sum_{i=1}^n \left\lfloor \frac{pi+q}{r} \right\rfloor$$ can be evaluated in $O(\log n)$ time. See [Summation of Floor Function Series](#external-links) for a special case.

## Problems
- [It's a Mod, Mod, Mod, Mod World](https://open.kattis.com/problems/itsamodmodmodmodworld)

## External links
- [Summation of Floor Function Series](https://web.archive.org/web/20190720160446/http://mathforum.org/library/drmath/view/73120.html)
- [Concrete Mathematics: A Foundation for Computer Science, 2nd Edition](http://www.informit.com/store/concrete-mathematics-a-foundation-for-computer-science-9780201558029), Chapter 3.5, Floor/Ceiling Sums.