whole number means 正整数,IF整数Ｉt is too easy.I do it　

with whole number.You know wiles,you are mathematician We can use simple number thory to solve it.It is easy to get it x=2^30, y=2^18 ,z=2^13 sytisfying the equation.LCM(3,5,7)=3*5*7=105,at last we have x=2^(30+35m),y=2^(18+21m),z=2^(13+15m)sytisfying the equation.m=0,1,2....,the solutions are infinite solutions.
Good Luck.