求證明方法 (餘數)

Let A = aY + R1
　 B = bY + R2
　 C = cY + R3
A x B x C = (aY + R1)(bY + R2)(cY + R3)
　　　　 = [(a+b)Y + R2 x aY + R1 x bY + R1 x R2](cY + R3)
　　　　 = (a+b+c)Y + R3 x (a + b)Y + R2 x (a+c)Y + R2 x R3 x aY + R1 x (b + c)Y +
　　　　　　R1 x R3 x bY + R1 x R2 x cY + R1 x R2 x R3
when A x B x C is divided by Y, by distribution law, all terms except R1 x R2 x R3 is divisible by Y. Hence, the remainder is R1 x R2 x R3 / Y,

i.e.The remainder of A x B x C / Y = (The remainder of A / Y x The remainder of B / Y x The remainder of C / Y ) / Y