实数范围x^n-1=(x-1)[x^(n-1)+x^(n-2)+……+x+1]复数范围x^n-1=(x-1)(x-x1)(x-x2)……[x-x(n-1)]其中x1=cos(2π/n)+isin(2π/n)x2=cos(4π/n)+isin(4π/n)……x(n-1)=cos[2(n-1)π/n]+isin[2(n-1)π/n]...
实数范围,当n为偶数时,设n=2m
x^n-1=x^2m-1=(x^2)^m-1=(x^2-1)[(x^2)^(m-1)+(x^2)^(m-2)+……+(x^2)+1]
=(x-1)(x+1)[x^(2m-2)+x^(2m-4)+……+(x^2)+1]
实数范围,当n为奇数数时
x^n-1
=(x-1)[x^(n-1)+x^(n-2)+……+x+1]