证明：（1）当n=1时,a^(n+1)+(a+1)^(2n-1)=2^2+a+1显然,a^(n+1)+(a+1)^(2n-1)能被a^2+a+1整除；（2）假设当n=k时,a^(k+1)+(a+1)^(2k-1)能被a^2+a+1整除那么,当n=k+1时,a^(n+1)+(a+1)^(2n-1)=a^(k+2)+(a+1)^(2k+1)=a^...