请教两道数学题

马丽

对那些除来除去的题总是做错。。。麻烦哪位帮我看看这两道吧？第一题完全无从下手。。。

1、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.

答案是C

2、What is the remainder when the positive integer x is divided by 6?

(1) When x is divided by 2, the remainder is 1; and when x is divided by 3, the remainder is 0.

(2) When x is divided by 12, the remainder is 3.

答案是D

bluegrassR

1.
(1) 2 is not a factor of n. 说明n是奇数，n-1和n+1都能被2整除，并且两个连续偶数必有一个能被4整除，所以（n-1)(n+1)能被8整除
(2) 3 is not a factor of n. 三个连续正整数必有一个能被3整除，如果n不能被3整除，则n-1和n+1必有一个能被3整除
综合1）2），则有n能被24整除，余数为0

bluegrassR

2.
1) x=2a+1=3b,把x写成x=6m+N的形式，取满足条件2a+1=3b下x的最小值，N=3，所以x=6m+3,被6除余3
2) x=12a+3，x被6除余3

马丽

茅塞顿开啊~~~非常感谢啊！！！感激涕零啊~~~~