有两个公式 a5+b5=(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)
a5-b5=(a-b)(a^4+a^3b+a^2b^2+ab^3+b^4)
原式x^8+x^6+x^4+x^2+1=(x^2-1)(x^8+x^6+x^4+x^2+1)/(x^2-1)
=(x^10-1)/(x^2-1) =(x^5+1)(x^5-1)/(x^2-1)
=(x+1)(x^4-x^3+x^2-x+1)(x-1)(x^4+x^3+x^2+x+1)/(x^2-1)
=(x^4-x^3+x^2-x+1))(x^4+x^3+x^2+x+1)