取余运算满足以下规则:(x + y) % p = (x % p + y % p) % p
证明如下:
假设: x = a * p + b; y = c * p + d; 则: x % p = b; y % p = d; 则: (x + y) % p = (a * p + b + c * p + d) % p = ((a + c) * p + (b + d)) % p = (b + d) % p = (x % p + y % p) % p