设m,n,p为任意非负整数,证明x^2+x+1|x^3m+x^(3n+1)+x^(3p+2)如果会的话加悬赏啊……_其他解答

设m,n,p为任意非负整数,证明x^2+x+1|x^3m+x^(3n+1)+x^(3p+2)
如果会的话加悬赏啊……

人气：410 ℃　时间：2020-05-29 04:29:39

解答

x^3m+x^(3n+1)+x^(3p+2)=x^3m-1+x^(3n+1)-x+x^(3p+2)-x^2+1+x+x^2=(x^3-1)(1+x^3+...+x^(3m-3)) + x(x^3-1)(1+x^3+...+x^(3n-3)) +x^2(x^3-1)(1+x^3+...+x^(3p-3))+1+x+x^2=(x-1)(1+x+x^2)(1+x^3+...+x^(3m-3)) + x(...