I need to be able to back up a server on a nightly basis, therefore I
need to be able to do so without getting prompted for a password.

I have copied the server's (where the backup crontasks exist)
id_rsa.pub file contents to the backup server's authorized_keys file.
With this setup I still get prompted for the password, and therefore
the crontasks silently fail.

I have also tried to create a bash file that contains the rsync
command preceded by RSYNC_PASSWORD=xxx, but I still get prompted for a
password.

What else am I missing?

Thanks for the help