and![\[(x-y)[f(x)+f(y)]\leqslant f(x^2-y^2), \forall x,y \in \mathbb{R}\]](http://latex.artofproblemsolving.com/8/0/b/80bb1d7a992c9683a0c2a07b2febe6271f4e60f5.png)
such that 
,
and 
.
is prime, 
with 
and 
Y by
Let 
be an acute triangle with circumcircle 
such that 
. Let 
be the midpoint of the arc 
of~ containing the point~
, and let 
be the other point on such that 
. Points 
and 
are chosen on sides 
and 
of the triangle such that 
and 
. Prove that 
.
be an acute triangle with circumcircle 
such that 
. Let 
be the midpoint of the arc 
of~ containing the point~
, and let 
be the other point on such that 
. Points 
and 
are chosen on sides 
and 
of the triangle such that 
and 
. Prove that 
.
is cyclic
which gives us 
,
.
,
,
is an isosceles trapezium.
,
is similar to 
by spiral similarity.
is cyclic.
.
.
and the assertion follows.
