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

[AdrianZ]

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.

 

[verty]

The trick is to realize that:

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