and 
Find the minimum 
satisfying![\[f(x+f(y))=x+f(f(y))\]](http://latex.artofproblemsolving.com/8/d/a/8daa6bcb3155768ee1ba4bd22beb53a85a6e3923.png)
and 
,
.
be positive odd integers. Prove that 
doesn't divide 
.
:
such that:
for all x,y E 
Y by Adventure10, Mango247
Let 
be a convex quadrilateral 
and 
a point inside it. The feet of the perpendiculars from to 
are 
respectively. The feet of the perpendiculars from to the sides of 
, the quadrilateral 
, are 
, where 
Prove that 
is similar to S.
be a convex quadrilateral 
and 
a point inside it. The feet of the perpendiculars from to 
are 
respectively. The feet of the perpendiculars from to the sides of 
, the quadrilateral 
, are 
, where 
Prove that 
is similar to S.
is cyclic and we get:
and furthermore we have 
and similarly 
so 
![\[ \left(\triangle{OC_4D_4}\sim \triangle {OCD} \;\; ,\;\;\triangle{OD_4A_4}\sim \triangle {ODA}\;\;, \;\; \triangle{OB_4C_4}\sim \triangle {OBC} \;\; ,\;\;\triangle{OA_4B_4}\sim \triangle {OAB} \right)\Rightarrow ABCD \sim A_4B_4C_4D_4 \]](http://latex.artofproblemsolving.com/7/a/2/7a25e3985ed16e96c1ff54f322dc58592bb64772.png)
