be an integer. Prove that 
is not a perfect cube of an integer.
such that
such that for all 
,![\[f(x+yf(x))+y = xy + f(x+y).\]](http://latex.artofproblemsolving.com/c/f/3/cf3d20a041c27244e90876119b4568b7a3e13c03.png)
board. Julia
Y by Adventure10
Problem 4. Let 
be the circumcircle of 
, and 
the point on the arc 
which do not pass through 
. 
and 
are the centers of incircles of 
and 
, respectively. Proove that the circumcircle of 
touches iff ![\[ \frac{AD}{BD}=\frac{AC+CD}{BC+CD}. \]](//latex.artofproblemsolving.com/6/e/c/6ecd7f774aa8c836e91371236aab9b8f9fd7221c.png)
Stoyan Atanasov
be the circumcircle of 
, and 
the point on the arc 
which do not pass through 
. 
and 
are the centers of incircles of 
and 
, respectively. Proove that the circumcircle of 
touches iff ![\[ \frac{AD}{BD}=\frac{AC+CD}{BC+CD}. \]](http://latex.artofproblemsolving.com/6/e/c/6ecd7f774aa8c836e91371236aab9b8f9fd7221c.png)
Stoyan Atanasov
This post has been edited 1 time. Last edited by imortal, May 31, 2006, 3:07 PM
and 
meet the circumcircle of 
at 
,
.
and 
(1).
is harmonical (or 
)
