I've noticed today that when I reboot my modem I get the same IP. Power off does not help. For various reasons about every week I reboot it for a new IP. Are others getting this - is this the new standard?
For various reasons, (mostly boring operational reasons to do with efficient content delivery and performance), IP addresses are very 'sticky'. That is, they will look and behave a lot like static IP addresses but you can't actually RELY on them not changing.
As far as your DSL router is concerned, the public IP address is being assigned by the PPP negotiation.