费费section7 两道相似题

windweed

7-23 n 和k均为正整数, N 能被K整除?

!) 2n 能被k整除

2)N^2能被K 整除

答案: E

7-67  Is 30 a factor of N?

1) 30 is a factor of N^2

2) 30 is a factor of 2N

答案:A

这两题具有相似性. 答案却不同. 我觉得第23题: N^2能被K 整除不充分, 已经包括了n=30的情况, 为什么答案不同了? 看了解释, 不是很明白, 是不是每次有具体数字时,规律都不一样?

还请指点指点!!谢谢.

pengh

for 7-23,

n=2 and k=4 satisfy (1) and (2) but 2 is not divisible by 4.

for n=any other number, n is divisible by k if (1) and (2) are satisfied.

for 7-67

If n can be written as n=a*b*c*..., a,b,c are prime numbers, then n is divisible by k.

windweed

以下是引用pengh在2004-12-29 3:18:00的发言：

for 7-67

If n can be written as n=a*b*c*..., a,b,c are prime numbers, then n is divisible by k.

谢谢pengh, 但是67, 我还是在犯迷糊.再想想.

windweed

我觉得既然23题的B不充分,  67里的A 也不充分.

67: 我想: 30是N^2的因子, 那么N^2同时含有2*3*5的因子, 再往后怎么得出N 可被30 整除就不确定了.

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你知道我在等你吗?

我只有一个人苦苦地想

pengh

because the power on each factor of 30 is 1. And each factor which appears on N^2 must appear at least once, and each factor of 30 appears only once, so it must be true that 30 is a factor of N if 30 is a factor of N^2.

For a counter example, 90=2*3^2*5, here the power on 3 is 2, more than 1. Here 90 is a factor of 30^2 but not 30.

Read the explanation at feifei again.

charmant

N^2分解质因式，因为能被三十整除

所以N^2的因子里面必含2，3，5

（我不知道该怎么解释了。。。比方说把30换成60，拆成2,2,3,5。N可以只含2，3，5，N^2就能拆出两个2，一个3，一个5，所以60能被N^2整除但不一定被N整除，但是30不行，若N^2能拆成2,3,5则至少必须含有两个2，两个3，两个5才行）

语言表达能力不好

charmant

7-23 n 和k均为正整数, N 能被K整除?

!) 2n 能被k整除

2)N^2能被K 整除

这个不明白！选E？给个反例？!多谢

adaqiu

1, n=3, k=2, 2n can be divided by k, but n cann't be divided by k

2. n=3, k=9, n^2 can be divided by k, but n cann't be divided by k

charmant

被K

没看清。。。谢谢楼上！！

windweed

谢谢pengh, 谢谢Charmant, 我基本是明白了. 解释的很好.