x^3+x^2+x+1=0,则x^97+x^98+x^99+.x^103=

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x^3+x^2+x+1=0,则x^97+x^98+x^99+.x^103=x^3+x^2+x+1=0,则x^97+x^98+x^99+.x^103=x^3+x^2+x+1=0,则x^97+x^98+x

x^3+x^2+x+1=0,则x^97+x^98+x^99+.x^103=
x^3+x^2+x+1=0,则x^97+x^98+x^99+.x^103=

x^3+x^2+x+1=0,则x^97+x^98+x^99+.x^103=
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