such that 
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 the inner angle bisector of the triangle 
. The perpendicular on the side 
at the point 
intersects the outer bisector of 
at point 
. The circle with center and radius 
intersects the sides 
and 
at points 
and 
respectively. 
-symmedian of 
intersects the circumcircle of again at point 
. Prove that the circumcircles of and 
are tangent.
be the inner angle bisector of the triangle 
. The perpendicular on the side 
at the point 
intersects the outer bisector of 
at point 
. The circle with center and radius 
intersects the sides 
and 
at points 
and 
respectively. 
-symmedian of 
intersects the circumcircle of again at point 
. Prove that the circumcircles of and 
are tangent.This post has been edited 2 times. Last edited by parmenides51, Dec 12, 2018, 6:36 AM
Reason: name typo
Reason: name typo
