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请教一道PREP 数学DS 题

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楼主
发表于 2008-7-25 16:34:00 | 只看该作者

请教一道PREP 数学DS 题

How many different prime numbers are factors of the positive integer n ?

 

(1) Four different prime numbers are factors of 2n.

 

(2) Four different prime numbers are factors of n2.

答案:B

沙发
发表于 2008-7-25 18:45:00 | 只看该作者
Condition 1. 2n has four different prime number factors. If 2 was originally not a factor of n, n has 3 factors. If 2 was originally a factor of n, then n has 4 factors.
example : n=3*5*7, 2n=2*3*5*7 vs.  n=2*3*5*7, 2n=2^2*3*5*7.

Condition 2. n^2 has four prime factors, so n has four prime factors. Again set n=2*3*5*7 n^2=2^2*3^2*5^2*7^2. n^2 still has four prime factors : 2,3,5,7
板凳
 楼主| 发表于 2008-7-25 22:50:00 | 只看该作者
 thanks!
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