当n=1时,显然x^1-y^1=x-y它能被x-y整除.假设当n=k时,x^k-y^k能被x-y整除,则当n=k+1时x^(k+1)-y^(k+1)=x^(k+1)-x^k*y+x^k*y-y^(k+1)=x^k(x-y)+y(x^k-y^k)显然x-y整除x^k(x-y),而由假设x-y能整除x^k-y^k所以x-y能整除...