Let a be a non zero number and m and n be integers. Prove by induction that:
(1)
(2).
can anyone explain me the basis and inductive steps here?
Do I have to start by supposing in (1) and
in (2)?
what about the inductive step?
If you don't know what exponentiation is, you have no hope of proving anything about it. (Not saying you don't know how to exponentiate--just that your book/prof is not expecting you to prove this without giving you something to start from. Look in your chapter or ask your prof what you're allowed to assume about exponentiation to begin with.)
When , holds since
For induction hypothesis, assume , where and are integers.
We begin by .
Multiplying through by a, we obtain .
Plug in the assumption for the left handside in the parethesis, we obtain
. The result is as desired.
Consequently, by induction hypothesis for all integers and .