how should I correct my update mistakes

How to add gpg repository keys

To add your keys, please try this:

Open a Terminal from the menu Applications → Accessories → Terminal and type or better copy and paste a row a time then press enter:
(if the system ask you a password give your user password, you will not see nothing when you type it, then press enter)

sudo apt-key adv --recv-keys --keyserver keyserver.ubuntu.com 40976EAF437D05B5

Then type: (when the system ask you a password give your user password, you will not see nothing when you type it, then press enter)

-------------------------

Then please copy and paste here the content of your /etc/apt/sources.list still using terminal type:

gedit /etc/apt/sources.list

Thank you

Please also using teminal BEFORE to send us the content of your /etc/apt/sources.list try to update your system... might be all ok now...

If the error still exists, please run this in terminal:

cat /etc/apt/sources.list > update.txt
sudo apt-get update >> update.txt

and attach file "update.txt" form you home folder here.

dear Mr. Marco , here is the result of my terminal input as you requested me,
thank you so much

# deb cdrom:[Ubuntu 10.04.1 LTS _Lucid Lynx_ - Release i386 (20100816.1)]/ lucid main restricted
# See http://help.ubuntu.com/community/UpgradeNotes for how to upgrade to
# newer versions of the distribution.

## Major bug fix updates produced after the final release of the
## distribution.

## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu
## team. Also, please note that software in universe WILL NOT receive any
## review or updates from the Ubuntu security team.

## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu
## team, and may not be under a free licence. Please satisfy yourself as to
## your rights to use the software. Also, please note that software in
## multiverse WILL NOT receive any review or updates from the Ubuntu
## security team.

## Uncomment the following two lines to add software from the 'backports'
## repository.
## N.B. software from this repository may not have been tested as
## extensively as that contained in the main release, although it includes
## newer versions of some applications which may provide useful features.
## Also, please note that software in backports WILL NOT receive any review
## or updates from the Ubuntu security team.
# deb http://us.archive.ubuntu.com/ubuntu/ lucid-backports main restricted universe multiverse
# deb-src http://us.archive.ubuntu.com/ubuntu/ lucid-backports main restricted universe multiverse

## Uncomment the following two lines to add software from Canonical's
## 'partner' repository.
## This software is not part of Ubuntu, but is offered by Canonical and the
## respective vendors as a service to Ubuntu users.

deb http://archive.canonical.com/ubuntu lucid universe
deb http://tw.archive.ubuntu.com/ubuntu/ lucid universe main
deb http://security.ubuntu.com/ubuntu/ lucid-security universe main
deb http://tw.archive.ubuntu.com/ubuntu/ lucid-updates universe main

dear Mr. Marco , here is the result of my terminal input as you requested me,
thank you so much

# deb cdrom:[Ubuntu 10.04.1 LTS _Lucid Lynx_ - Release i386 (20100816.1)]/ lucid main restricted
# See http://help.ubuntu.com/community/UpgradeNotes for how to upgrade to
# newer versions of the distribution.

## Major bug fix updates produced after the final release of the
## distribution.

## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu
## team. Also, please note that software in universe WILL NOT receive any
## review or updates from the Ubuntu security team.

## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu
## team, and may not be under a free licence. Please satisfy yourself as to
## your rights to use the software. Also, please note that software in
## multiverse WILL NOT receive any review or updates from the Ubuntu
## security team.

## Uncomment the following two lines to add software from the 'backports'
## repository.
## N.B. software from this repository may not have been tested as
## extensively as that contained in the main release, although it includes
## newer versions of some applications which may provide useful features.
## Also, please note that software in backports WILL NOT receive any review
## or updates from the Ubuntu security team.
# deb http://us.archive.ubuntu.com/ubuntu/ lucid-backports main restricted universe multiverse
# deb-src http://us.archive.ubuntu.com/ubuntu/ lucid-backports main restricted universe multiverse

## Uncomment the following two lines to add software from Canonical's
## 'partner' repository.
## This software is not part of Ubuntu, but is offered by Canonical and the
## respective vendors as a service to Ubuntu users.

deb http://archive.canonical.com/ubuntu lucid universe
deb http://tw.archive.ubuntu.com/ubuntu/ lucid universe main
deb http://security.ubuntu.com/ubuntu/ lucid-security universe main
deb http://tw.archive.ubuntu.com/ubuntu/ lucid-updates universe main

Have you run the command from the 1st comment?
sudo apt-key adv --recv-keys --keyserver keyserver.ubuntu.com 40976EAF437D05B5

Thanks Dmitry Shachnev, that solved my question.

New to Ubuntu: read the Ubuntu Manual, it's very informative: http://ubuntu-manual.org/
Click on the "download Button" to download the latest PDF version.
The online help https://help.ubuntu.com/10.04/index.html

Relax and fun:
http://planet.ubuntu.com/ and Full Circle Magazine http://fullcirclemagazine.org/

thank you

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