Equality formulas and Properties

Basic nature:

(1) If p | (a-B), a then B (% P ). For example, 11 limit 4 (% 7), 18 limit 4 (% 7)

(2) (a % P) = (B % P) means a ≡ B (% P)

(3) symmetry: A between B (% P) is equivalent to B between a (% P)

(4) transmission: If a contains B (% P) and B contains C (% P), A contains C (% P)

 

Calculation rules:

The modulo operation is similar to the basic four arithmetic operations, but the Division is an exception. The rules are as follows:
(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)
AB % P = (a % P) B) % P (4)

Combination rate: (a + B) % P + C) % P = (a + (B + C) % P (5)

(A * B) % P * C) % P = (A * (B * C) % P (6)

Exchange rate: (a + B) % P = (B + a) % P (7)

(A * B) % P = (B * A) % P (8)

Allocation rate: (a + B) % P * C) % P = (A * C) % P + (B * C) % P (9)

Important theorem: If a contains B (% P), then for any C, there are (A + C) values (B + C) (% P); (10)

If a contains B (% P), all C (A * C) contains (B * C) (% P); (11)

If a then B (% P), C then D (% P), then (A + C) Then (B + d) (% P), (a-c) round (B-d) (% P ),

(A * C) round (B * D) (% P), (A/C) round (B/d) (% P); (12)

If a contains B (% P), any C has AC contains BC (% P); (13)

 

 

Second group nature:

1. If, thenM| (A−B), HereM| (A−B) Indicates (A−B) Can beMDivision

2. If, then

3. If ,,,

4. If

5. If AC hybrid BC (mod m) and C and M are mutually compatible, a hybrid B (mod m)