x^24-1的最小多项式?这是一个八次域希望会算的人能给与帮助

Question

x^24-1 的最小多项式?这是一个八次域 希望会算的人能给与帮助

Answer 1

x^24-1
=(x^12-1)(x^12+1)
=(x^6-1)(x^6+1)(x^4+1)(x^8-x^4+1)
=(x^3-1)(x^3+1)(x²+1)(x^4-x²+1)(x^4+1)(x^8-x^4+1)
=(x-1)(x²+x+1)(x+1)(x²-x+1)(x²+1)(x^4-x²+1)(x^4+1)(x^8-x^4+1)
=(x-1)(x+1)(x²+1)(x²+x+1)(x²-x+1)(x^4-x²+1)(x^4+1)(x^8-x^4+1)