Gfilui

I am trying to install Java on my system.

when i run
sudo apt-get install default-jdk

I get

E: Unable to locate package default-jdk

and before that i used
sudo apt-get update && apt-get upgrade

and got:

>Ign:1 http://ppa.launchpad.net/fossfreedom/packagefixes/ubuntu yakkety InRelease 
.
.
.
Err:16 http://ppa.launchpad.net/fossfreedom/packagefixes/ubuntu yakkety/main amd64 Packages
 404 Not Found
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.
.
yakkety/main DEP-11 64x64 Icons
Err:26 http://ppa.launchpad.net/jonathonf/vlc/ubuntu yakkety/main i386 Packages
 404 Not Found
.
.
.
Fetched 2,802 B in 18s (154 B/s)
Reading package lists... Done
W: The repository 'http://ppa.launchpad.net/fossfreedom/packagefixes/ubuntu yakkety Release' does not have a Release file.
N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use.
N: See apt-secure(8) manpage for repository creation and user configuration details.
W: The repository 'http://ppa.launchpad.net/jonathonf/vlc/ubuntu yakkety Release' does not have a Release file.
N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use.
N: See apt-secure(8) manpage for repository creation and user configuration details.
E: Failed to fetch http://ppa.launchpad.net/fossfreedom/packagefixes/ubuntu/dists/yakkety/main/binary-amd64/Packages 404 Not Found
E: Failed to fetch http://ppa.launchpad.net/jonathonf/vlc/ubuntu/dists/yakkety/main/binary-i386/Packages 404 Not Found
E: Some index files failed to download. They have been ignored, or old ones used instead.

I also tried fixing the PPA repositories but i'm not exactly sure i'm in the right direction with this.

How do i solve this?

It happened to me before, although my release version was a supported one (sometimes oracle repo updates Java and ppa tries to download installer from the old link).

In this link you can see the following:

Ubuntu 16.10 Yakkety Yak is no longer supported by Canonical (and thus, Launchpad and this PPA). The PPA supports Ubuntu 17.10, 17.04, 16.04, 14.04 and 12.04.

Although, if you require to install Java in Ubuntu, I'd rather recommend to install directly .tar.gz file from here, follow the instructions for installing, you just need to uncompress .tar.gz file and update alternatives for Java as this link explain.