求教几个Property of integers的问题！涛涛GWD-3-9/15/16/36,能给讲讲吗？

3-9: if r is a constant and a_n=r * n for all positive integers n, for how many values of n is a_n<100?

1) a₅₀=500

2) a₁₀₀+a₁₀₅=2,050

题目看不太懂，所以牢烦NN给解释一下。

3-15: If n and k are positive integers, is n/k an even integer?

1) n is divisible by 8

2) k is divisible by 4

我选的是c，其实没有真正理解他们之间的关系，please any NN?

3-16: 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.

同上题是同样的问题。

3-36：If M is the least common multiple of 90,196, and 300, which of the following is NOT a factor of M?

A. 600

B. 700

C. 900

D. 2100

E. 4900

除了代入法，还有什么好的方法吗？

麻烦大家了，谢谢！

哪位能抽空给讲讲？

僅供參考。

1。提供的條件能把r算出來就行。

2。給n,k隨便找個數就會發現C不行。

3。24=3* 2^3。條件1告訴你(n-1)(n+1)可以整除8﹐條件2告訴你可以整除3。兩個合起來就可除24。

4。把所有的數都拆成質因子的乘積可能會快點。

sorry,i still couldnot get ur point on question 3-16.

why (n-1)(n+1)can be divisible by 8 if 2 is not a factor of n,and it can be divised by 3 since 3 is not a factor of n........

could you please instruct me more detaily?

2 is not a factor of n, so n is odd. n-1 & n+1 are consecutive even numbers. one of them can be divisible by 4. So the product can be divisible by 8.

条件2不是说不可以整除3吗？

 条件2不是说不可以整除3吗？

定理：如果一自然数不能被3整除，则这个数的平方被三除余一

        即 N^2 除以３余１　

　　所以 N^2-1=(N+1)(N-1） 能被3整除