consistent random order

I am returning results ordered randomly using 'order by random()'. My issue has to do with page numbers in our web application. When I hit the 2nd page and retrieve results with an offset, ordering by random() isn't really what I want since I will often receive results that were on the 1st page (they get re-randomized).

I'm looking for a way to order in a controled random order. Maybe a UDF. Ideally I would need to do this:

ORDER BY myRandomUDF(1234)
or
ORDER BY myRandomUDF(2345)

Where the argument acts like a seed that always returns a consistent pseudo-random set. That way, when I get to the 2nd page, i know i'm getting the dataset back in the same order that I had on page 1, and the offset works like normal. Is this even realistically possible?

Thanks,
Jeff Herrin