请教PREP数学

sss000

n, y are positive integers and 450y=n^3, which of the following must be an integer?
I. y/(3*2^2*5)
II. y/(3^2*2*5)
III. y/(3*2*5^2)


A. None
B. I only
C. II only
D. III only
E. I, II, III




求教啊。450=5^2*3^2*2
按理来说应该是II和III都对啊。。。先深深感谢各位大侠的帮助！

sdcar2010

450y=n^3

2*(5^2)*(3^2)*y = n^3

n = a*2*5*3

y= b*(2^2)*3*5

Only I has to be an integer.

sss000

Hey, I understand that you can get2*(5^2)*(3^2)*y = n^3

but how did the following you get from the last step?
n = a*2*5*3


Also, from this step how did you get y= b×2^2×3×5
why 2^2??


Thanks!!

sdcar2010

If 2 is a factor of n^3, then 2 must be a factor of n.  
If 3 is a factor of n^3, then 3 must be a factor of n.
If 5 is a factor of n^3, then 5 must be a factor of n.
So n = a*2*3*5

Then 450y=n^3 = (a*2*3*5)^3; y=a^3*2^2×3×5 = b*2^2×3×5

sss000

拜谢大侠

xiaoyu90922

厉害厉害！！遇到这种题，是不是从答案给的因子出发去凑呀？