Just installed Catalina and cannot update LO. I did allow apps downloaded from Anywhere!
“LibreOffice_7.0.3_MacOS_x86-64(1).dmg” is damaged and can’t be opened.
This message is quite clear - so
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Delete your downloaded LibreOffice_7.0.3_MacOS_x86-64(1).dmg files (you probably have more than one in your Downloads directory)
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Download again from https://download.documentfoundation.org/libreoffice/stable/7.0.3/mac/x86_64/LibreOffice_7.0.3_MacOS_x86-64.dmg.mirrorlist by manually selecting a download mirror nearby your location.
I did just that (from mirror.clarkson.edu), and nothing changed. Same response by Catalina.