If we set 
then it's the unique polynomial such that for all integers 
In general, for each positive integer k,there is a unique polynomial 
such that 
Find the value of 
for 
and 
if 
then find the coefficient of 
in 
Y by Adventure10, Mango247
Let 
be the orthocentre and 
be the circumcentre of an acute triangle 
. Let 
and 
be the altitudes of the triangle with 
on 
and 
on 
. Let 
. Let 
be the second point of intersection of the circumcircles of triangles 
and 
, and let 
be the midpoint of side 
. Prove that points 
are collinear if and only if is the circumcentre of triangle 
.
be the orthocentre and 
be the circumcentre of an acute triangle 
. Let 
and 
be the altitudes of the triangle with 
on 
and 
on 
. Let 
. Let 
be the second point of intersection of the circumcircles of triangles 
and 
, and let 
be the midpoint of side 
. Prove that points 
are collinear if and only if is the circumcentre of triangle 
.
