1.当n=1时原式=x^2-y^2=(x-y)(x+y)能被x+y整除故命题成立2.假设n=k时命题成立,即 x^(2k)-y^(2k)能被x+y整除当n=k+1时x^(2k+2)-y^(2k+2)=x·x^(2k+1)-y·y^(2k+1)=(x+y)[x^(2k+1)-y^(2k+1)]-y·x^(2k+1)+x·y^(2k+1)=...