It is known that X2+X+1=0, and the power of 2006 of X + the power of 2005 of X + the power of 2004 of X +...+ X2+ X +1

It is known that X2+X+1=0, and the power of 2006 of X + the power of 2005 of X + the power of 2004 of X +...+ X2+ X +1

X=-1
Original formula=1-1+1-1+...+1-1+1
=1

Given that the 2004 power of 1+x+x2+... x + the 2005 power of x =0, then the 2006 power of x =____

2004 Power of 1+x+x2+... x 2005 power of =0
(1+X)+x2(1+x)+.+x^2004(1+x)=0
(1+X)(1+x2+x^4+.x^2004)=0
Because:1+x2+x^4+.x^2004=0
So:1+x=0: x=-1
That is:2006 power of ×=1

2004 Power of 1+x+x2+... x 2005 power of =0
(1+X)+x2(1+x)+.+x^2004(1+x)=0
(1+X)(1+x2+x^4+.x^2004)=0
Because:1+x2+x^4+.x^2004=0
So:1+x=0: x=-1
I.e.2006 power of ×=1