只需讨论n为正偶数的情况.首先讨论n=2:显然x^2-y^2=(x+y)(x-y)可被（x+y）整除.然后假设n=k时x^k-y^k可被(x+y)整除,则当n=k+2时x^(k+2)-y^(k+2)=x^2(x^k-y^k)+x^2*y^k-y^(k+2)=x^2(x^k-y^k)+(x^2-y^2)y^k.由于(x^2-y...