Eu segui as instruções aqui: Como instalar o skype no ubuntu 16.04
O erro que recebi está abaixo. O Skype não está no meu menu, não consigo iniciá-lo, então devo ter falhado.
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W: The repository 'http://ppa.launchpad.net/eclipse-team/ppa/ubuntu xenial 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: An error occurred during the signature verification. The repository is not updated and the previous index files will be used. GPG error: http://deb.opera.com/opera stable InRelease: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY D615560BA5C7FF72
W: The repository 'http://archive.canonical.com/ubuntu saucy 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: Failed to fetch http://deb.opera.com/opera/dists/stable/InRelease The following signatures couldn't be verified because the public key is not available: NO_PUBKEY D615560BA5C7FF72
E: Failed to fetch http://ppa.launchpad.net/eclipse-team/ppa/ubuntu/dists/xenial/main/binary-amd64/Packages 404 Not Found
E: Failed to fetch http://archive.canonical.com/ubuntu/dists/saucy/partner/binary-amd64/Packages 404 Not Found [IP: 2001:67c:1562::1c 80]
W: Some index files failed to download. They have been ignored, or old ones used instead.
Acho que, para ser sincero, essa resposta está desatualizada. A Microsoft "atualizou" o SKype de modo que agora é, essencialmente, um front-end para uma coisa baseada na web. Não é um cliente no uso comum. Então, vá para a página do Skype hopme, link escolha o .deb e siga as instruções. Isso funciona.