functions

dusty6662002

For any positive integer x, d[x] denotes its smallast odd divisor and D[x] denotes its largest odd divisor. Is X even?

1. D[x] - d[x] = 0
2. D[3x] = 3

How can I get into it ? Can sb here enlight me a bit ?

songqi

题目说：正整数x，d(x)是最小奇因子，D(x)是最大奇因子。问x是否是偶数。

由条件1知，最小奇因子=最大奇因子，即x只有一个奇数因子。因为任何正整数都有1这个奇数因子，因此x可以表示成x=1*2^m,即x可以取1，2，4，8，16……，不能判断其为偶数；

由条件2知，3x的最大奇因子为3，因此3x可以表示成3x=3*2^m*1,即x=2^m,和条件1是等同的。

因此，我认为此题选E。

yankevi

我觉得这题选A，请教X只有一个奇数因子的话能区分最大和最小的奇数因子吗？

所以存在最大最小的奇数因子只能是在有2个及其以上的奇数因子中数比较

所以选A

atc

选E，取x=1，或2代入

dusty6662002

OA is E

sidong

1)D[x]-d[x]=0

it's possible only in case of D[x]=d[x]=1 (am I right?)

it means x has no odd divisors but 1....

x is even or 1.

2)D[3x]=3

3x doesn't have any odd divisor greater than 3

x doesn't have any odd divisor greater than 1

x is even or 1.

1+2) x is even or 1

So I prefer E as correct answer....

What's the answer given???