MathDB
I 2

Source:

May 25, 2007
floor functioninvariant

Problem Statement

Prove that for any positive integer nn, ⌊n3⌋+⌊n+26⌋+⌊n+46⌋=⌊n2⌋+⌊n+36⌋.\left\lfloor \frac{n}{3}\right\rfloor+\left\lfloor \frac{n+2}{6}\right\rfloor+\left\lfloor \frac{n+4}{6}\right\rfloor = \left\lfloor \frac{n}{2}\right\rfloor+\left\lfloor \frac{n+3}{6}\right\rfloor .
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