显然如果n被3整除,则n^2+1不能被3整除设如果n = 3t+1（t是整数）n^2+1 = 9t^2+6t+2=3(3t^2+2t)+2 则被3除余2如果n = 3t+2n^2+1 = 9t^2+12t+5 = 3(3t^2+4t+1)+2 则被3除余2可见不存在一个正整数n,使n^2+1能被3整除...