GWD31第四套15题求教（站内没查到，非常感谢！）

successwei

    

Q15:

    

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)     2 is
not a factor of n.

    

(2)     3 is
not a factor of n.

    

                                                                                                                              

    

A. Statement (1) ALONE is
sufficient, but statement (2) alone is not sufficient.

    

B. Statement (2) ALONE is
sufficient, but statement (1) alone is not sufficient.

    

C. BOTH statements TOGETHER
are sufficient, but NEITHER statement ALONE is sufficient.

    

D. EACH statement ALONE is
sufficient.

    

E. Statements (1) and (2) TOGETHER
are NOT sufficient.

sandy_phil

选c吧，条件1推出n为奇数，代入1，3，5。。。。可以得到仅当n=3时，余数为8，其余均余0。结合条件2可以得出r=0

马甲兮兮

数论的题目我来解答~~

首先，对所有n>1，n-1, n, n+1为3个连续整数，其中至少有一个能被3整除。如果n不能被3整除=>(n-1)(n+1)能被3整除；但无法判断是否能被24整除。

其次，对所有n>1, 如果n不能被2整除，则n-1，n+1均能被2整除。记n-1=2k，则n+1=2k+2, (n-1)(n+1)=2k*2k+2=2*2*k(k+1)，能被8整除（其中k*(k+1)能被2整除)，所以在此条件下，(n-1)(n+1)能被8整除；但不能判断时候能整除24。

因此1+2得出 (n-1)(n+1)整除24 （or remainder r=0) 

当n=1时，remainder=0。

mrgong775

还是赞成2楼的，考试时用代入法更好些

Hi_Cynthia

支持3楼！