First and Last Entry on a Page using Modulus Remainder

So I know it's quite a long title but I'm not sure what I'll be searching next time. It has taken me a lot longer than I thought it would mostly out of frustration and the inability to know exactly what I'm looking for... always difficult. After a cup of tea the solution was glaringly obvious, just do a primary school mathematics table and it all makes sense (see my 10 mod table below).

This article is a quick note (so I never spend as long again) in PHP on how to determine when looping through a loop, which entry was first and which was last. This is incredibly useful for pagination.

The Situation
I want the script to start writing a DIV layer in the code at the start of the loop (and at every first entry of a page). I want the script to close the DIV layer at the last entry of each page.

So I have a loop
Rather crude but it's a FOR loop for those old CMS's running PHP4:

for ($this_link_index=1; $this_link_index

The FIRST entry

if (($this_link_index % $links_per_page)==1) {
	//... do something for first entry ...
}

The LAST entry

if (($this_link_index % $links_per_page)==0) {
 //... do something for last entry ...
}

Based on:

1 mod 5 = 1
2 mod 5 = 2
3 mod 5 = 3
4 mod 5 = 4
5 mod 5 = 0
6 mod 5 = 1
7 mod 5 = 2
8 mod 5 = 3
9 mod 5 = 4
10 mod 5 = 0