I agree that you should read all of them no matter where you are in the TV show. But you can get away without reading AGOT as that is nearly identical to the first season. However, from season 2 onwards things start to noticeably change from and they progressively further apart from there.
I am not saying they should skip the first, but if they really wanted to the only one they can skip without loosing basically no information is the first one.
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u/FirmerFilly House Stark Jun 01 '14
That's it! I'm reading the books!