[求助]求教一道gwd数学~

xiangdingdan

The function f is defined for each positive three-digit integer n by f(n)=2^x3^y5^z, where x, y and z are the hundreds, tens, and units digits of n, respectively. If m and v are three-digit integers such that f(m)=9f(v), then m-v=?

 

求助各位nn丫~~想不到用什么办法来做额。。。

holddreams

here is my opinion

f(m)= 2^x * 3^y * 5^z

f(v)= 2^x' * 3^y' * 5^z'

=2^(x-x')* 3^(y-y') * 5^ (z-z')=9

so x-x'=0, z-z'=0, y-y'=2

y is the tenth digit of the three digit number. y-y'=2 is the tenth digit of the number (m-v)

x-x'=0 is the hunderd digit, and z-z' is the unit.

so m-v=20

xiangdingdan

嗯 就是这个答案~~ 太强悍啦~~

万分感谢吖~~~

weixiaozi09

厉害了~~