[問題]天山數學7-6

[mark-alan]

If a,b, k, and m are positive integers, is a^k a factor of b^m ?

(1) a is a factor of b

(2) k=m

小弟愚昧,有不符合(1)的嘛?

[汪汪北鼻]

If a,b, k, and m are positive integers, is a^k a factor of b^m ?

(1) a is a factor of b

(2) k=m

1)insufficient if a =2, b=4 but k=10 m=2, 2^10>4^2

2)insufficient if a>b, k=m, a^k>b^m

1)2) sufficient a<b, k=m, a^k<b^m

hence, the answer is C

[chris8888]

這麼說吧.
(1) a is a factor of b => 表示b/a=t, 而t是integer, 套用在b^m/a^k = t1, 理論上可以除盡, 但有個例外, m與k的關係誰大誰小將是關鍵.
若作為分子的b^m的m次方太小, a^k的k次方過大, 將會出現insufficient
舉例 : 9^1/3^4

(2) k=m 所以ETS, 才會再第二個選項告訴你k=m時候會怎樣?, 光第二個不行算出, 但已經給你一個概念

1+2 => 限訂了次方根的大小關係後, 呼之欲出, C