GWD 19-29

meckychen · 发表于 2010-1-4 16:40:58

Q29:

Is the integer n odd?

(1) n is divisible by 3.

(2) 2n is divisible by twice as many positive integers as n
.

Q29:

Is the integer n odd?

(1) n is divisible by 3.

(2) 2n is divisible by twice as many positive integers as n
.

Answer is B How to consider? Thank you.

a10285 · 发表于 2010-1-4 16:53:46

（1）举反例6
（2）若把N=x^a*y^b （a、b为质数）
若n奇，2n的因子数=（a+1）（b+1）（1+1）是n因子数（a+1）（b+1）两倍
若n偶，则设x=2，2n因子数=（a+1+1）（b+1）不等于2（a+1）（b+1）
因此只有在n奇的时候，（2）才成立

选B

meckychen · 发表于 2010-1-4 16:59:56

请问 2n is divisible by twice as many positive integers as n 是什么意思啊？

a10285 · 发表于 2010-1-4 17:21:54

2n的总因子数是n的两倍~~

meckychen · 发表于 2010-1-4 20:28:28

Thank you.

GWD 19-29

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