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Got the same error after updating from 2.3.1 -> 2.4.0.
Solution:
Create a new DB.
Backup/ dump the old DB.
Install a blank EE instanace into the new DB.
Import the old DB into the new one.
Error is gone.
If you compare new with the old DB structure, table “exp_remember_me” is indeed missing.
Here’s the Structure. Might save you lot of work.
CREATE TABLE `exp_remember_me` (
`remember_me_id` varchar(40) NOT NULL default '0',
`member_id` int(10) default '0',
`ip_address` varchar(16) default '0',
`user_agent` varchar(120) default '',
`admin_sess` tinyint(1) default '0',
`site_id` int(4) default '1',
`expiration` int(10) default '0',
`last_refresh` int(10) default '0',
PRIMARY KEY (`remember_me_id`),
KEY `member_id` (`member_id`)
) ENGINE=MyISAM DEFAULT CHARSET=utf8;
EllisLab Team: please fix your EE Update Script!