and the segment is 3. Find the possible minimum value of 
and 
Prove that
such that for any polynomial 
of degree 
with real coefficients, there exists a polynomial 
of degree at most 
and 
intersect at exactly 
be a convex quadrilateral. If 
are the midpoints of the segments 
,
,
and 
.
.
Y by Adventure10, Mango247
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:
![\[ n-3<{2d\over p}<\Bigl[{n\over2}\Bigr]\cdot\Bigl[{n+1\over 2}\Bigr]-2,\]](//latex.artofproblemsolving.com/6/e/e/6eea62bf3ef064f376ac03e6201927938c600e9f.png)
where![$ [x]$](//latex.artofproblemsolving.com/1/0/5/105f81f70e5e3f58e5cfff9e54072a0acdee0402.png)
denotes the greatest integer not exceeding 
.
be the sum of the lengths of all the diagonals of a plane convex polygon with 
vertices (where 
). Let 
be its perimeter. Prove that:![\[ n-3<{2d\over p}<\Bigl[{n\over2}\Bigr]\cdot\Bigl[{n+1\over 2}\Bigr]-2,\]](http://latex.artofproblemsolving.com/6/e/e/6eea62bf3ef064f376ac03e6201927938c600e9f.png)
where
![$ [x]$](http://latex.artofproblemsolving.com/1/0/5/105f81f70e5e3f58e5cfff9e54072a0acdee0402.png)
denotes the greatest integer not exceeding 
.
times. And each time the side appears it also includes two diagonals. Thus, 
.
