x^3+x^2+x+1=0,则x^97+x^98+x^99+.x^103=
问题描述：
x^3+x^2+x+1=0,则x^97+x^98+x^99+.x^103=
答
提公因式法吧x^97+x^98+x^99+x^100+x^101+x^102+x^103=x^97(1+x+x^2+x^3+x^4+x^5+x^6)因为1+x+x^2+x^3＝0所以原式＝x^97(x^4+x^5+x^6)=x^100(x+x^2+x^3)由1+x+x^2+x^3＝0→x+x^2+x^3＝-1原式＝－x^100...