用数学归纳法证x^2n-y^2n,能被X+Y整除
问题描述：
用数学归纳法证x^2n-y^2n,能被X+Y整除
答
n=1时x^2n-y^2n=x^2-y^2=(x+y)(x-y)能被X+Y整除设n≤k时,x^2n-y^2n,能被X+Y整除n=k+1时x^2n-y^2n=x^(2k+2)-y^(2k+2)=(x^2k-y^2k)(x^2+y^2)-x^2ky^2+x^2y^2k=(x^2k-y^2k)(x^2+y^2)-x^2y^2(x^(2k-2)-y^(2k-2))因为n≤k...