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
Let 
be a triangle and 
the midpoint of the side 
. On sides 
and 
, consider the points 
and 
, respectively, both different from the midpoints on the sides, such that 
and 
. Prove that 
.
be a triangle and 
the midpoint of the side 
. On sides 
and 
, consider the points 
and 
, respectively, both different from the midpoints on the sides, such that 
and 
. Prove that 
.
