such that 
be a monic polynomial with integer coefficient. And suppose there exist 4 distinct integer 
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 point inside 
, and let 
be a circle which contains and touches the legs 
and 
in points 
and 
respectively. Straight line 
parallel to from intersects in a point 
. Let 
be the intersection point of the ray 
and circumscribed circle of 
and 
. Prove that 
and 
is a tangent of the circumscribed circle of .
be a point inside 
, and let 
be a circle which contains and touches the legs 
and 
in points 
and 
respectively. Straight line 
parallel to from intersects in a point 
. Let 
be the intersection point of the ray 
and circumscribed circle of 
and 
. Prove that 
and 
is a tangent of the circumscribed circle of .This post has been edited 1 time. Last edited by parmenides51, Jun 21, 2022, 1:32 AM
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