n=1时a^2+(a+1) 满足
n=k时满足a^(k+1) *a+(a+1)^(2k-1) * a 能被a^2+a+1整除
n=k+1时
a^(k+1+1) +(a+1)^(2k+2-1)
= a^(k+1) *a + (a+1)^(2k-1)(a+1)^2
= a^(k+1) *a +(a+1)^(2k-1) (a^2+2a+1)
=a^(k+1) *a+(a+1)^(2k-1) * a + (a+1)^(2k-1) (a^2+a+1)
显然,上式左边部分和右边部分都能被a^2+a+1整除,所以整个式子能被整除
因此得证