Define an equivalence relation R on $\backslash$omega by mRn iff m and n have the same number of distinct prime factors. Prove there is a map f : $\backslash$omega $/$R $->\backslash$omega $/$R satisfying f$([$m$])=[$m$^2]$ but that there

is no map g : $\backslash$omega $/$R $->\backslash$omega $/$R satisfying g$([$m$])=[3$m$].$