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[n/2] [n/3] [n/4] =n^2 , floor function

Source: 2018 Chile National Olympiad level 2 p4

October 22, 2022
floor functionalgebranumber theoryfunction

Problem Statement

Find all postitive integers n such that ⌊n2⌋⋅⌊n3⌋⋅⌊n4⌋=n2\left\lfloor \frac{n}{2} \right\rfloor \cdot \left\lfloor \frac{n}{3} \right\rfloor \cdot \left\lfloor \frac{n}{4} \right\rfloor=n^2 where ⌊x⌋\lfloor x \rfloor represents the largest integer less than the real number xx.
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