#### furthermathishard

##### New member

- Joined
- Mar 19, 2020

- Messages
- 2

Posted below is the original question:

I have already solved (probably incorrectly?) part (a), and am now attempting to write the proof for part (b)

I understand that I need to dissociate the base 3 into the factors that make it up, for instance

If N is even, then (anan-1 ... a1a0)3 = (2m)10

= 3^m x an + 3^m-1 x an-1...3a1+a0

= 3(3^m-1 x an + 3^m-2 x an-1...a1) + a0

Then I separated it into two cases:

1) if the sum of the terms in the bracket is odd

3 x even = even

even + odd/even = even

2) if the sum of the terms in the bracket is even

3 x odd = odd

odd + odd = even

odd + even = odd

so a0 is odd?

I have no idea how to continue from this point on, and this is only the proof from one direction ://

Please help if you know how to solve this!!