Keep the Intel coolers, Intel requires returning the the original boxed heatsink with the CPU if you have to RMA it, the heatsink coolers have a SN on them matched to a corresponding number on the original Intel boxed CPU.
You need to keep the box and the heatsink that originally came with the CPU.
As far as I known AMD doesn't do this and I don't know when Intel actually started it, but its definitely 775 series.