AoPS Academy
is called frameable if it is possible to draw a regular polygon with 
sides all whose vertices lie on these lines, and no line contains more than one vertex of the polygon.
are frameable.
is not frameable.
is frameable.
, determine all polynomials 
with integer coefficients such that 
divides 
for every positive integer .
with the smaller base 
are constructed the squares 
and 
. Prove that the perpendicular bisector of passes through the midpoint of 
.
such that
for all real numbers 
satisfying the equation
+1 w
be the center of a circle inscribed in triangle 
, in which 
and 
. The points 
and 
were marked on the rays 
and 
so that 
. Prove that the line 
passes through the point .
be the center of a circle inscribed in triangle , in which and . The points and were marked on the rays and so that . Prove that the line passes through the point .
