prep ds 2-166

haileywang

166.


If the prime numbers p and t are the only prime factors of the integer m, is m a multiple of p2t ?

(1) m has more than 9 positive factors.

(2) m is a multiple of p3.

【答案】B

【思路】

t are the only prime factors of the integer m,m沒有其他質因數,故m為t所組成,有可能為m=t,m=t^2.................
(1) m has more than 9 positive factors 可知m＞t^9, 但無法知道和p的關係,NOT sufficient
(2) m is a multiple of p^3,p為m的質因數,又t are the only prime factors of the integer m,t=m, m is a multiple of p^3 ,可以写成m is a multiple of p2t,sufficient

无法理解上面那句话~~感觉前面是不是少了p and t。。。

haileywang

嗯嗯嗯。。。got it...thx

piacia

不是nn，但回答一下

注意谓语的是are，表语是factors，故题意为p和t是m的唯一的两个质因子

提干：p, t为质数，m整数，p和t为m唯一质因子, 问m/(tp^2)是否为整数？
解：设x为余下因子乘积，即xpt=m，则m/(tp^2)=xpt/(tp^2)=x/p，看能否判断x/p是否为整数

1)m有多余9个的正数因子——不相关条件，显然不能判断x/p是否为整数，不充

2)m=p^3——计算m/(tp^2)=p^3/(tp^2)=p/t，p, t为质数，显然p/t不为整数，充分

答案B