and 
.
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 
.
and 
be two sequences of integers such that 
and 
for all 
.
divides 
for an infinity of integers 
such that 
for all 
are coprime. Consider the sequence 
given by 
.
such that 
is even and 
is an integer. Prove that the numerator in its simplest form of 
is an odd integer greater than 
.
Y by ehuseyinyigit
Triangle 
satisfies 
. Let the incenter of triangle be 
, which touches 
at 
, respectively. Let 
be the midpoint of 
. Let the circle centered at passing through 
intersect 
at 
, respecively. Let line 
meet at 
, line 
meet 
at 
. Prove that the three lines 
are concurrent.
satisfies 
. Let the incenter of triangle be 
, which touches 
at 
, respectively. Let 
be the midpoint of 
. Let the circle centered at passing through 
intersect 
at 
, respecively. Let line 
meet at 
, line 
meet 
at 
. Prove that the three lines 
are concurrent.This post has been edited 1 time. Last edited by pokmui9909, Mar 30, 2025, 5:29 AM
lie on angle bisector of 
.
are symmetric about angle bisector of 
where 
and 
meet at 
.
is cyclic, so simson on 
and 
finishes it i guess
