模运算

A * B) mod C = (A mod C * B mod C) mod C

乘法示例：

让 A=4, B=7, C=6

让我们验证：(A * B) mod C = (A mod C * B mod C) mod C

LHS= 等式的左边

LHS= 等式的右边

LHS = (A * B) mod C

LHS = (4 * 7) mod 6

LHS = 28 mod 6

LHS = 4

RHS = (A mod C * B mod C) mod C

RHS = (4 mod 6 * 7 mod 6) mod 6

RHS = (4 * 1) mod 6

RHS = 4 mod 6

RHS = 4

LHS = RHS = 4

 

(A + B) mod C = (A mod C + B mod C) mod C

示例：

让 A=14, B=17, C=5

让我们证明：(A + B) mod C = (A mod C + B mod C) mod C
LHS = 等式左边
RHS = 等式右边

LHS = (A + B) mod C
LHS = (14 + 17) mod 5
LHS = 31 mod 5
LHS = 1

RHS = (A mod C + B mod C) mod C
RHS = (14 mod 5 + 17 mod 5) mod 5
RHS = (4 + 2) mod 5
RHS = 1

LHS = RHS = 1