大侠 证明能被7整除的特征若7|(AnAn

AnAn-1…A3A2A1
=AnAn-1…A6A5A4*1000+ A3A2A1
=AnAn-1…A6A5A4*1000-A3A2A1*1000+1001*A3A2A1
=1000*(AnAn-1…A6A5A4－A3A2A1)+1001*A3A2A1
因为1001A3A2A1=7*143**A3A2A1
所以1001A3A2A1能被七整除
根据已知AnAn-1…A6A5A4－A3A2A1也能被七整除
所以1000*(AnAn-1…A6A5A4－A3A2A1)+1001*A3A2A1能被七整除
所以(AnAn-1…A3A2A1)能被七整除