be a positive integer.Prove that there is a polynomial 
with integer coefficients so that 
,![$$a^{2n+1}+b^{2n+1}+c^{2n+1}=abc[P(a,b)+P(b,c)+P(a,c)]$$](http://latex.artofproblemsolving.com/5/2/0/520813bebb2f297928208f7b7b2eea76d24043ac.png)
.
.
Y by
Given a circle with center 
, and square 
. Point 
and 
are on the circle, and 
is tangent to the circle at point 
. Let 
represent the midpoint of 
and 
represent the intersection between and circle. Prove that 
.
, and square 
. Point 
and 
are on the circle, and 
is tangent to the circle at point 
. Let 
represent the midpoint of 
and 
represent the intersection between and circle. Prove that 
.Attachments:
