当n = 1,x^2n - 1 = (x + 1)(x - 1),原命题成立
假设n = k时,命题成立,x ^2k - 1 = A(x + 1),得x^2k = A(x + 1) + 1
n = k + 1时,x^2n - 1 = x^2k * x^2 - 1 = A*x^2*(x + 1) + x^2 - 1 =
A*x^2 *(x + 1) + (x + 1)(x - 1) = A'(x + 1),命题也成立
所以原命题成立