pp-T2-DS2

[Huang Hsin-Yi]

2. 140-!-item-!-187;#058&000076
If k is a positive integer, is k the square of an integer?

(1) k is divisible by 4.

(2) k is divisible by exactly four different prime numbers.

Ans:E

感覺上B選項就可判斷k is not square of an integer

[Huang Hsin-Yi]

有沒有高手會呀???

[amazingslim]

if k=2*3*5*7=>k is not the square of an integer
if k=2^2*3^2*5^2*7^2=>k is the square of an integer

[Huang Hsin-Yi]

if k=2*3*5*7=>k is not the square of an integer
if k=2^2*3^2*5^2*7^2=>k is the square of an integer

你的意思
也就是說k=4*9*25*49 這樣怎會是 4 個不同prime的乘積勒

[amazingslim]

你的意思
也就是說k=4*9*25*49 這樣怎會是 4 個不同prime的乘積勒

題目是說k is divisible by exactly four different prime numbers.
並沒有k is the product of exactly four different prime numbers.

我的理解是k剛剛好可以被四個質數整除，質數可以是好幾次方，也可以包含非質數(但是該數不能分解為四個質數其他質數)
ex.k=2*3*5*7*20 (20=2^2*5)

又例如
20 is divisible by exactly two different prime numbers.
不代表20=2*5

[Huang Hsin-Yi]

真是一語驚醒豬腦袋
感謝大師提點!!