证明：（1）n=1时，为x^2-y^2=(x-y)(x+y)，能被x+y整除。（2）假设n=k时，原命题成立，即x^2k-y^2k=(x+y)*p当n=k+1时，x^(2k+2)-y^(2k+2)=x^2*(y^2k+(x+y)*p)-y^(2k+2)=y^2k*(x^2-y^2)+x^2*(x+y)*p=y^2k*(x+y)(x+y)+x^2*(x+y)*p，能被x+y整除综上X的2n次方减去Y的2n次方能被X加Y整除
