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?

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- March 24th 2010, 06:01 PMserious331Math Induction
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? - March 25th 2010, 07:43 AMTinyboss
Exactly what properties of exponentiation are you given to work with?

- March 25th 2010, 07:57 AMserious331
- March 25th 2010, 08:01 AMTinyboss
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.) - March 26th 2010, 02:24 PMnovice
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 .