[/quote]
,
.
be the intersection point of the diagonals 
meets 
and 
(where 
)
at 
.
is perpendicular to 
.
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![\[ x^2 + y = p^n \]](http://latex.artofproblemsolving.com/5/b/d/5bd672934a395aabd6865ca4b50d8da75c0fe07e.png)
For 
positive integers and 
being a prime.
and 
.
Equality holds when 
or 
lie on a circle 
such that 
.
intersect again at 
.
Equality holds when 
intersect its circumcircle 
.
determine a triangle 
,
is relative to 
are concurrent at a point 
and that 
and 
.
lie in the interiors of segments 
respectively, such that 
Let 
intersect 
at 
,
intersect 
at 
.
and 
are either parallel or coincide.
and 
.
Where 
such that :
.
be reals such that 
Prove that 
Let 
Prove that 
be a fixed integer. There are 
beads on a circular necklace. You wish to paint the beads using 
colors, such that among any 
consecutive beads every color appears at least once. Find the largest value of 
for which this task is 
possible.
Y by Adventure10, Mango247
Let 
be a unit square. Draw a quadrant of the a circle with 
as centre and 
as end points of the arc. Similarly, draw a quadrant of a circle with 
as centre and 
as end points of the arc. Inscribe a circle 
touching the arc 
externally, the arc 
externally and also touching the side 
. Find the radius of .
be a unit square. Draw a quadrant of the a circle with 
as centre and 
as end points of the arc. Similarly, draw a quadrant of a circle with 
as centre and 
as end points of the arc. Inscribe a circle 
touching the arc 
externally, the arc 
externally and also touching the side 
. Find the radius of .
and 
such that 
be center of 
then,
