當(dāng)n=1時(shí),顯然x^1-y^1=x-y它能被x-y整除.假設(shè)當(dāng)n=k時(shí),x^k-y^k能被x-y整除,則當(dāng)n=k+1時(shí)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)顯然x-y整除x^k(x-y),而由假設(shè)x-y能整除x^k-y^k所以x-y能整除...