[/quote]
,
such that for all 
,
is a prime number, 
are natural numbers 
)
.
.
be the midpoint of 
on triangle 
.
lies on segment 
such that 
and 
on line 
such that 
.
.
there exists a unique positive integers 
such that 
is a square of a rational number.
for which![\[2^p = 2^{q-2} + q!.\]](http://latex.artofproblemsolving.com/8/8/2/88270dc4aa4a54cc8b2e525b7d9d940c300e49ac.png)
.
are positive numbers, then prove that
Prove that
Where 
,
and 
are parallel. Angle bisectors of 
and 
intersect at 
.
and 
meet again at 
.
.
and 
such that 
and 
is a prime number
.
such that for all any 
Y by Adventure10, Mango247
Let 
be an acute angled triangle and let 
be its circumscribed circle. A point 
is given in the interior of the triangle, such that 
, where 
and 
are on and lies on 
while lies on 
. Prove that is on the angle bisector of 
if and only if 
.
be an acute angled triangle and let 
be its circumscribed circle. A point 
is given in the interior of the triangle, such that 
, where 
and 
are on and lies on 
while lies on 
. Prove that is on the angle bisector of 
if and only if 
.
since 
is bisector of 
and is easy to see that: 
since 
since 
and 
