MathDB

2

Part of PEN I Problems

Problems(1)

I 2

Source:

5/25/2007
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 .
floor functioninvariant