**6**

x^1001-1 is divisible by x-1

if we divide x^4 + x^3 + 2x^2 + x + 1 by x-1

(x^4 + x^3 + 2x^2 + x + 1)/(x-1)=x3+2x2+4x+5 and a reminder of 6

in other words,

x^4 + x^3 + 2x^2 + x + 1=(x-1)*(x3+2x2+4x+5)+6

we should consider x>1, if x=1, we get zero