MathDB
How many integers does it take to screw in a cube?

Source: 2017 AIME I #13

March 8, 2017
2017 AIME I

Problem Statement

For every m≥2m \geq 2, let Q(m)Q(m) be the least positive integer with the following property: For every n≥Q(m)n \geq Q(m), there is always a perfect cube k3k^3 in the range n<k3≤m⋅nn < k^3 \leq m \cdot n. Find the remainder when ∑m=22017Q(m) \sum_{m = 2}^{2017} Q(m) is divided by 1000.
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