模运算规则
运算规则 模运算与基本四则运算有些相似,但是除法例外。其规则如下: (a + b) % p = (a % p + b % p) % p (1) (a – b) % p = (a % p – b % p) % p (2) (a * b) % p = (a % p * b % p) % p (3) (a^b) % p = ((a % p)^b) % p (4) 结合律: ((a+b) % p + c) % p = (a + (b+c) % p) % p (5) ((a*b) % p * c)% p = (a * (b*c) % p) % p (6) 交换律: (a + b) % p = (b+a) % p (7) (a * b) % p = (b * a) % p (8) 分配律: ((a +b)% p * c) % p = ((a * c) % p + (b * c) % p) % p (9) 重要定理: 若a≡b (% p),则对于任意的c,都有(a + c) ≡ (b + c) (%p);(10) 若a≡b (% p),则对于任意的c,都有(a * c) ≡ (b * c) (%p);(11) 若a≡b (% p),c≡d (% p),则 (a + c) ≡ (b + d) (%p),(a – c) ≡ (b – d) (%p), (a * c) ≡ (b * d) (%p),(a / c) ≡ (b / d) (%p); (12)