Let

be the sum of the lengths of all the diagonals of a plane convex polygon with

vertices (where

). Let

be its perimeter. Prove that:
where
![[x]](/media/m/6/a/4/6a47dfb91475b9d5490dbb3a666604a3.png)
denotes the greatest integer not exceeding

.
%V0
Let $d$ be the sum of the lengths of all the diagonals of a plane convex polygon with $n$ vertices (where $n>3$). Let $p$ be its perimeter. Prove that:
$$n-3<{2d\over p}<\Bigl[{n\over2}\Bigr]\cdot\Bigl[{n+1\over 2}\Bigr]-2,$$
where $[x]$ denotes the greatest integer not exceeding $x$.