I've seen pretty much the same description at the page A theorem of number theory.

I'm having trouble understanding that theorem ; the first examples that comes to mind isa=12,b=3,b=4 so that none of the parts make sense to me.

I also don't get the proof of the first part as to meashould be bigger thanborcso thatsandtshould be a fraction (ie: 2/3), not an integer.

I'm really stuck there and in a rush preparing for an exam

Thank you kindly for your help