AoPS Academy
+2 w
where 
is a positive integer and 
is a prime.(Don't get mad at me,I've used the search function and did not see a correct and complete solution anywhere.)
+1 w
such that 
divides 
for all positive integers 
and 
with 
.
be the Fermat point of a 
. Prove that the Euler line of the triangles 
, 
, 
are concurrent and the point of concurrence is 
, the centroid of .
until 
such that 
is equilateral now, taking as homothetic center the midpoint of 
(3:1) sending X to circumcenter of , P to centroid of and A to centroid of 
that's enough
tan 
.