And what I know of the i3 it's generally sold as a 64-bit processor.
http://en.wikipedia.org/wiki/Intel_Core
The AMD part in the name of the 64-bit Ubuntu's has to do with the protocol used, it was developed by AMD and later became the industry standard for *68 processors.
Because Intel likes to be standard compliant I'm sure the 64-bit (AMD) version of Kubuntu runs on your computer
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