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 an acute triangle inscribed in a circle 
and let 
be the midpoints of segment 
, of segment 
and minor arc 
of , respectively. Let 
and 
be points in such that 
and that 
.
a) Prove how that the line joining the centers of the circumscribed circles of the triangles
and 
, is parallel to .
b) If
and intersect at 
, and 
and intersect at 
, prove that 
is parallel to .
be an acute triangle inscribed in a circle 
and let 
be the midpoints of segment 
, of segment 
and minor arc 
of , respectively. Let 
and 
be points in such that 
and that 
.a) Prove how that the line joining the centers of the circumscribed circles of the triangles
and 
, is parallel to .b) If
and intersect at 
, and 
and intersect at 
, prove that 
is parallel to .
