The function f is defined for each positive three digit integer n by f(n)

=2^x3^y5^z ( 2 的x次方乘以 3 的y 次方乘以5的z次方，where x,y and z are the

hundreds, tens, and unit digit of n, respectively. If m and v are three-

digit positive integer such that f(m)=9f(v), then m-v=?

key 20

完全没有思路。。。

因为f(m)=9f(v) ，设m的百十个位分别为X1,Y1,Z1;v的百十个位分别为X1,Y1,Z1。则f(m)=2^(x1)3^(y1)5^(z1)=9* 2^(x2)3^(y2)5^(z2)=2^(x2)3^(y2+2)5^(z2)所以X1=X2,Y1-Y2=2,Z1=Z2,因此M-V=20