prep数学题考古，达人相助.......................................

tuoier

1. If n is a multiple of 5 and n=p^2乘以q,  which of the following must be a multiple of 25?

a. p^2
b. q^2
c. p乘以q
d. p^2乘以q^2
e. p^3乘以q

答案是D，求思路……

alancui

As n = p^2 * q, and can be divided by 5.


=>5|p = 0, or 5|q = 0


if 5|p = 0, 25|p^2 = 0, thus, 25|p^2*q^2 = 0
if 5|q = 0, 25|q^2 = 0, thus, 25|p^2*q^2 = 0

1. If n is a multiple of 5 and n=p^2乘以q,  which of the following must be a multiple of 25?

a. p^2
b. q^2
c. p乘以q
d. p^2乘以q^2
e. p^3乘以q

答案是D，求思路……

-- by 会员 tuoier (2012/2/6 23:37:00)

candykim

因为n是5的倍数，而n=p^2乘以q，随意p,q这两个数一定至少其中一个含有因数5
而现在找25的倍数，所以p^2乘以q^2，把这两个数都平方了，就一定存在25的倍数~所以选D