PP-DS T1 Q169

[小花]

169
If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a^n, what is the value of a?
(a) a^n=64
(b) n=6

Ans: B


麻煩各位了

[mupeane]

1x2x3x4x5x6x7x8=2^7x3^2x5x7為a^n的倍數

(1)a^n=2^6 or 8^2 有兩個解
(2)單獨成立

[chris8888]

列出 1*2*3*4*5*6*7*8 = 2^7 * 3^2 * 5 * 7

(a) a^n=64
找可能成為64的值 ;
1. 2^6 = 64
2. 4^3 = 64
3. 8^2 = 64

有三種情形可以是64, insufficient.

(b) n=6
當n = 6 時, 根據 2^7 * 3^2 * 5 * 7
只有2^7可以包含住, 其他factors沒有這樣多次方可以用.

[小花]

很清楚 謝謝兩位的回覆