How to prove this?

1. Sep 20, 2011

If $$a^x|b^y$$ & $$xt-yz\geq 0$$ then $$a^z|b^t$$

This is not a homework. I found this theorem in a book without having proved it, so I wondered how it could be proved.

2. Sep 20, 2011

verty

The trick is to realise that:

if xt >= yz, then b^(yz) | b^(xt)