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Amazon doesn't have a 1-click trademark. They have a patent on it.
They list it as a trademark:
http://www.amazon.com/gp/help/customer/display.html/ref=footer_cou?ie=UTF8&nodeId=508088
That page doesn't specify if it is also a registered trademark, but some licensees, including Apple, explicitly state that it is a registered trademark of Amazon.com, Inc:
http://www.apple.com/legal/trademark/appletmlist.html
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