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The message was revealed as a hoax and Facebook removed the fan page Wednesday without comment.
Graham Cluley, senior technology consultant at computer security company Sophos, said there are a number of ways a hacker could have gained access to Zuckerberg's page.
"It's not clear if he was careless with his password, was phished, or sat down in a Starbucks and got sidejacked while using an unencrypted wireless network, but however it happened, it's left egg on his face just when Facebook wants to reassure users that it takes security and privacy seriously," Cluley said.