怪怪的 OG 解答

[Tony]

請教一題OG,DS#243
If the interger n is greater than 1, is n equal to 2?
(1)n has exactly two positive factors.
(2)The difference of any two distinct positive factors of n is odd.

答案為B..... :o

OG 對於(2) 的解釋說到:
if n>2 and n is odd, then 1 and n are factors of n whose difference is even.---->小弟完全同意 :D

if n>2 and n is even, then 2 and n are factors of n whose difference is even.----->怪怪的耶 :-$

ㄟ,為何是even?
例如:14>2, 14=2*7 but difference is 7-2=5 odd
24>12,24=2*12 whose difference is 12-2=10 even

故(2) not sufficient 選 E, 可是錯了... :'(
那兒出錯了?還是哪位有另解看法呀?? 謝謝

[micht]

if n>2 and n is even, then 2 and n are factors of n whose difference is even.----->怪怪的耶

ㄟ,為何是even?

ie) 4>2 4的factor有1,2,4 所以4-2=2 even~ 如果n>2為even的話 difference可為even or odd...

B) is sufficient 因為2的factor=1,2 2-1=1 odd 沒有例外..

[汪汪北鼻]

我試著來解釋一下，你的想法並沒有錯，你的結論也沒有錯，問題是你所討論的是大於２的情況，可能是even也可能是odd，換言之，題目是問n是否為２，既然大於２情況有even有odd，那就討論２，２的factors是１和２，二個相減為１是odd，所以（２）充分，故 選之！:D

[Tony]

唉ㄞ~~真是點悟了我
謝謝micht and airforce667...
可以不必抱著疑惑入眠... :P

Thanks a lot & have a nice dream!!!