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 the midpoint of the hypotenuse 
of a right triangle ABC. Let 
be the circle passing through 
and touching 
at 
. Similarly, let 
be the circle passing through 
and touching 
at 
, where and lie on the same side of the line . Prove that the line 
passes through the midpoint of arc of the circumcircle of 
.
be the midpoint of the hypotenuse 
of a right triangle ABC. Let 
be the circle passing through 
and touching 
at 
. Similarly, let 
be the circle passing through 
and touching 
at 
, where and lie on the same side of the line . Prove that the line 
passes through the midpoint of arc of the circumcircle of 
.This post has been edited 2 times. Last edited by parmenides51, Nov 25, 2020, 6:05 AM
