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I'm not sure what the best solution is. I know that I am a registered user at Amazon US and that when I went to buy a book that was only available on their UK web site the site recognized me when I logged in. That being said, they have a nice cross-website recognition system of users but a search on the US site did not yield the book I was looking for.
You'll be hard pressed to determine where the customer is located so I suggest you go for the simple approach and provide both links. You could cite the above example as part of the reason why you provide both if need be.
There are ways to accomplish this but I think lorax is right, for now I would just offer both links. If you want to take a look at a thread on this very subject there's one here.
Getting the users country from the ip address [webmasterworld.com]
Regarding Amazon, why not setup two links below your offer/review.
One telling to "Buy it now from Amazon.co.uk" and the other like "Get it from Amazon.com". Works on one of my sites OK.