# Homework Help: Base b (not 10) proof (<=)

1. Jun 29, 2010

### Noxide

1. The problem statement, all variables and given/known data

Whenever base b is even (b=2k for some integer k) a number H=(d(n-1)d(n-2)...d1d0)b is even <=> d0 is even.

2. Relevant equations

3. The attempt at a solution
I have formulated a proof for the forward direction (=>) but I am having trouble getting started on a proof for the backwards direction (<=) starting with the fact that d0 is even.
Any advice would be much appreciated. I know all the definitions I'm just unsure how to build from d0 is even.

2. Jun 29, 2010

### Staff: Mentor

You don't show what you've done, so this might or might not be useful.

H=(d(n-1)d(n-2)...d1d0)b
= d(n-1) * bn - 1 + d(n-2) * bn - 2 + ... + d1*b + d0

You have d0 being even. What can you say about b raised to any positive power? Is it even or odd? What about multiples of even or odd numbers?

3. Jun 29, 2010

### Noxide

even * even = even always
odd * even = even always
even + odd = odd

I think my problem was identifying the problem correctly

I rewrote it this way

b = 2k, k is a natural number, H=(d(n-1)d(n-2)...d1d0)b is even <=> do is even

shouldnt be too hard from there