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ID card, registration letter etc. What you would expect really.

Are you from the UK? You use the word university which most Americans don't use. If so, buying online gets you a better deal compared to in store.
 
I don't know what their policies are and if they have changed, but in Fall 2007 after I purchased my Mac in March '07, I was at the local Apple Store and was surprised to see that they did not offer Education pricing for software. At least that was what I was told. It was a difference of $7 and I was a little naive, so I just bought it. Now, I'd just buy it on Apple's site or Amazon (w/free .edu Prime) and save the difference.

I always wondered if they only matched hardware prices, none, or if my experience was just an anomaly
 
My girlfriend and I went to get our new computer (MBP 13") about two months ago. She is currently in grad school so all we had to do was show her Student ID. I do believe they may run the name or something else once they have it behind the desk or at least make sure the name is up to date.
 
In my experience they do not ask for ID at all, I purchased a mac at an apple store, and the only thing they asked me was for the name of the school, and the zip code ( which i had to look up online, on the computers they had at the store).
 
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