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 HWenslawski, Mango247
Circles 
and 
are externally tangent to each other at 
. A random line 
cuts at 
and 
and at 
and 
(points 
are in this order on ). Line 
meets again at 
and line 
meets again at 
. Prove that the radical axis of circles 
and 
is parallel to .
(Vlad Robu)
and 
are externally tangent to each other at 
. A random line 
cuts at 
and 
and at 
and 
(points 
are in this order on ). Line 
meets again at 
and line 
meets again at 
. Prove that the radical axis of circles 
and 
is parallel to .(Vlad Robu)
This post has been edited 2 times. Last edited by AngleChasingXD, Mar 16, 2021, 2:31 PM
?
be the inversion with center 
and for each 
let 
.
.
