充分性：已知n|m成立,即有m=qn.则2^m-1=2^qn-1=(2^n-1)(2^n(q-1)+2^n(q-2)+...+2^n+1)=(2^n-1)k所以2^n-1|2^m-1必要性：已知：2^n-1|2^m-1成立则有2^m-1=(2^n-1)k=(2^n-1)(2^n(q-1)+2^n(q-2)+...+2^n+1)=2^qn-1则有2...