作业帮提问GMAT余数题,实在数学差,希望指点!
来源：学生作业帮 编辑：作业帮 分类：英语作业 时间：2024/05/09 15:48:21
提问GMAT余数题,实在数学差,希望指点!
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.
请问这题思路是什么啊?怎么利用那两个条件,我完全无从下手
（n+1)(n-1)，中间是相乘，我多余打了个*
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.
请问这题思路是什么啊?怎么利用那两个条件,我完全无从下手
（n+1)(n-1)，中间是相乘，我多余打了个*
Answer:
According to the given condition,we have
(n-1)(n+1)-r = 24m,
where m is an integer,and therefore,
r = n²-1-24m.
1.Let m=0,n=3,we have r=8.Note that 2 is not a factor of n when n=3.
2.Let m=0,n=2,we have r=3.Note that 3 is not a factor of n when n=2.
According to the given condition,we have
(n-1)(n+1)-r = 24m,
where m is an integer,and therefore,
r = n²-1-24m.
1.Let m=0,n=3,we have r=8.Note that 2 is not a factor of n when n=3.
2.Let m=0,n=2,we have r=3.Note that 3 is not a factor of n when n=2.