Can't download and open a PDF file

"but won't download or open"

It has to be downloaded first before you can open it, and you said you can't download in either, so let's start there. Are viewing the pdf through Safari or Chrome or Firefox? If you received it as an email attachment, what program do you use to read your email? How did you try to download it, and what folder are you trying to put it in?

~ Jane

And how do you know otherwise that the file is not damaged?

Downloading the file is not part of what Adobe Acrobat Reader does itself. If you got this message, something was actually downloaded to your system. Otherwise, you wouldn't have gotten this message. I assume you downloaded the file from some website? Or perhaps it was an e-mail attachment? Often such damage is due to the file actually being a zero length file (i.e.0 bytes long), a ZIP file that first needs to be decompressed, or possibly an e-mail attachment that was encoded in some unexpected manner by the sender's e-mail client, expecting your e-mail client to know about said encoding. 

In any case, without a sample of such a file, there isn't much we can do here to assist you.