of positive integers such that
such that![\[ x f(x + xy) = x f(x) + f \left( x^2 \right) f(y) \quad \forall x,y \in \mathbb{R}.\]](http://latex.artofproblemsolving.com/b/0/f/b0f1a1d3b9de5d23f1b5a2e9be3b88d8bd575883.png)
over 
is linear
and 
Prove that
Y by Adventure10, Mango247
In the convex pentagon 
all interior angles have the same measure. Prove that the perpendicular bisector of segment 
, the perpendicular bisector of segment 
and the angle bisector of 
intersect in one point.
all interior angles have the same measure. Prove that the perpendicular bisector of segment 
, the perpendicular bisector of segment 
and the angle bisector of 
intersect in one point.
,
,
is intersection of perpendicular bisector of segments 
is bisectors in 
is incenter of 
,
and 
,
be the intersection of the two perpendicular bisectors. Then the perpendicular bisectors of 
and 
bisect 
and 
,
;
,
is an angle bisector of 
.
