MathDB

4

Part of 2018 Chile National Olympiad

Problems(1)

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

Source: 2018 Chile National Olympiad level 2 p4

10/22/2022
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.
floor functionalgebranumber theoryfunction