be a monic polynomial with integer coefficient. And suppose there exist 4 distinct integer 
such that 
.
such that 
such that ![\[f(2x+y) + f(x+f(2y)) = f(x)f(y) - xy\]](http://latex.artofproblemsolving.com/0/6/2/0623b7c328af6d088cfc5dd288afe3e17a94ff29.png)
for all reals 
and 
.
sastifying 
Y by Adventure10, Mango247
Let 
be a fixed circle. Find all finite sets 
of points on with the following property:
For any point
on , one can partition into two sets 
and 
such that the sum of distances from to the points in equals the sum of distances from to the points in .
be a fixed circle. Find all finite sets 
of points on with the following property:For any point
on , one can partition into two sets 
and 
such that the sum of distances from to the points in equals the sum of distances from to the points in .
