# A sum involving the greatest-integer function

## TL;DR

This paper investigates the properties of a specific sum involving the greatest-integer function, analyzing how its values change as parameters vary.

## Contribution

It characterizes the set of values of a sum involving the greatest-integer function for varying n and x, providing new insights into its behavior.

## Key findings

- Identifies the structure of the set of possible sum values.
- Provides formulas or bounds for the sum.
- Analyzes the sum's behavior as n and x vary.

## Abstract

We determine properties of the set of values of $ [nx] - ([x]/1 + [2x]/2 + \cdots + [nx]/x) $ as $n$ and $x$ vary.