8.

Let a, b integer, 1 < a < b

Let c = rounded up to the next integer

Let k, m integer, m > 0, k >= 0

a [4] m >= c * (b + k) -> a [4] (m + k + 1) >= b [4] (k + 2)

Proof:

http://www.scrybqj.com/scrybqjdocuments/..._proof.pdf

I hope I'll find some time to put this content in Tex.

Let a, b integer, 1 < a < b

Let c = rounded up to the next integer

Let k, m integer, m > 0, k >= 0

a [4] m >= c * (b + k) -> a [4] (m + k + 1) >= b [4] (k + 2)

Proof:

http://www.scrybqj.com/scrybqjdocuments/..._proof.pdf

I hope I'll find some time to put this content in Tex.