证明:当n=1时,x^2n-y^2n=x²-y²=(x+y)(x-y)结论成立现假设当n=k时,结论成立,即x^2k-y^2k能被x+y整除.无妨设x^2k-y^2k=M(x+y).于是x^2(k+1)-y^2(k+1)=x^(2k+2)-y^(2k+2)=x²x^2k-y²y^2k=x²x^2...