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
, 
, 
and 
are points on the sides 
, 
and respectively, so that the lines 
, 
and 
would intersect at a point 
. If 
is a point on the segment 
, show that 
and are collinear, if and only if
, , and are points on the sides , and respectively, so that the lines , and would intersect at a point . If is a point on the segment , show that and are collinear, if and only if
