the root of x^2+x+1 is : W , W^2 ( OMEGA is the cube root of unity = (-1 + or - roots *i)/2)

since x^2+x+1 divide x^a+x^b+1
then roots of x^2+x+1 are roots of x^a+x^b+1
===>
w^a+w^b+1=0
or w^a+w^b=-1
we know from properties of omega that w^(3n-1) + w^ (3n-2)=-1
for all natural number n
then a = 3n-1 and b = 3n-2 , n element of N= natural number

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