MathDB

A7

Part of VMEO III 2006 Shortlist

Problems(1)

A problems related to floor function

Source: VMEO III

10/15/2015
Prove that for all n∈Z+n\in\mathbb{Z}^+, we have ∑p=1n∑q=1p⌊−1+8q+(2p−1)22⌋=−n(n+1)(n+2)3 \sum\limits_{p=1}^n\sum\limits_{q=1}^p\left\lfloor -\frac{1+\sqrt{8q+(2p-1)^2}}{2}\right\rfloor =-\frac{n(n+1)(n+2)}{3}
number theoryfloor functionalgebrafunction