Multiple Hit Counter? (PHP)

I want to make a links page on my flash site and be able to record how many people click on each link. I don’t need to show the results, I only need to be able to record them and access them from the server.

I don’t want to use a separate hit counter for each link - it would be ideal if all of the hits could be stored in a single txt file that I could download and read.

I was wondering if the PHP hit counter posted on this site could be modified to suit my needs.

Any ideas?