x12+x9+x6+x3+1 =(x^15-1)/(x^3-1) =(x^5-1)/(x-1) * (x^10-x^5+1)/(x^2+x+1) =(x^4+x^3+x^2+x+1) * (x^8-x^7+x^5-x^4+x^3-x+1)
