If a and b are the roots of x^2+x+1=0, what is the equation with roots a^19 and b^7?

a^2 = - (a + 1)

so a^3 = -(a^2 + a) = 1

so a^19 = a

similiary

b^7 = b

so roots are a^19 and b^7=> a and b are roots so eqution is x^2+x+1= 0