prep-math

If n is a positive integer and r is the remainder when (n-1)(n+1) is divided by 24, what is the value of r ?

(1) n is not divisible by 2

(2) n is not divisible by 3

答案c，数学奇差，想不懂，求大家指教~~

(1)===>n is old. (n-1) and (n+1) are even. In two consecutive even number, there is a multiple of 4. So (n-1)(n+1) is a multiple of 8. (*A*)

(2)n is not divisible by 3, In any three consecutive number there is one multuple of 3, so (n-1)(n+1) is a multiple of 3. (*B*)

(*A*) AND (*B*), so (n-1)(n+1) is a multiple of 24.

厉害~~谢谢了~~