请教天山9-16

monicars

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.

MINE A

ANS:C

各位有什么看法?

windfalls

答案是C

解法如下：

因为n不是2、3的倍数，故n=6k+1或者6k-1。

于是(n+1)(n-1)=n^2 -1=(6k +/- 1)^2 -1 = 36 k^2 +/- 12k =12k(3k +/-

1)

这里 +/- 表示加或者减

若k是偶数，则 12k 是24的倍数；若k是奇数，则 3k +/- 1是偶数，上式仍

然是24的倍数。

故在C的条件下，余数r只能为0。

sportman

我是先从(n-1)n(n+1)必然是3的倍数来考虑的, 但没有找到什么好办法,所以就列举了

既然N不能被3除,也不能被2除 我就列举了 , 发现(n-1)(n+1) 在n=5,7,11,13,17....时都可以被称24整除,所以reminder r=0

因此C对.

不知道我的解法对不对.

daoying

C

A 不能成立, 当n为3, 5的时候余数都不一样