[/quote]
,
and 
such that 
is divisible by 
?
be a triangle with incenter 
,
and 
at 
and 
.
and 
the reflections of 
be the intersection of 
with 
,
be the midpoint of 
and 
are perpendicular.
be a convex quadrilateral with perpendicular diagonals intersecting at 
.
be three diameters of the circumcircle of an acute triangle 
be an arbitrary point in the interior of 
,
be the orthogonal projection of 
,
be the point such that 
is the midpoint of 
,
be the point such that 
,
be the point such that 
.
is similar to triangle 
such that for any 
,
real numbers 
there exists real numbers 
such that 
for at least 
indices 
.
and 
denotes the fractional part of 
.
be an acute-angled scalene triangle. Let 
and 
be points on the rays 
and 
,
.
and 
be points on the rays 
and 
,
.
and 
intersect at 
,
is parallel to 
be the circumcircle of a triangle 
the midpoints of the sides 
,
the midpoint of the arc 
and 
intersect the perpendicular bisectors of 
and 
intersect at 
.
.
is equal to the largest prime divisor of 
.
such that, for all positive real numbers 
,
and 
,
,
,
.
of positive integers that satisfy the equation: 
.
be the set of real numbers. Determine all functions 
such that ![\[ f(x^2 - y^2) = x f(x) - y f(y) \]](http://latex.artofproblemsolving.com/6/8/f/68f78e0df627f6ac04052433c01627bf16f0af8e.png)
for all pairs of real numbers 
and 
,
to be the total number of times the digit 
between 
and 
.
,
,
,
.
Y by
Let 
. Two subsets 
and 
of 
are said to be friends if the following conditions are true:
that are friends such that each one of them contains at least 
elements.[/quote]
. Two subsets 
and 
of 
are said to be friends if the following conditions are true:- They do not share any elements.
- They both have the same number of elements.
- The product of all elements from equals the product of all elements from .
that are friends such that each one of them contains at least 
elements.[/quote]This post has been edited 1 time. Last edited by Titibuuu, Today at 8:58 AM
