well, you have to prove three conditions as you know: that the relation you've defined is reflexive, symmetric and transitive. the reflexive and symmetric is trivial. for the transitive, suppose

and for some then

are you assuming that is fixed? (i'm quite sure the answer is no because otherwise the claim would be trivially false in general!)

However the author proceeds: Does the analogous statement hold if one replaces 2 by some arbitrary power ? (supposedly the first statement was ~ is an equivalence relation).