Steve,
Welcome to nixCraft forum!
Yes a script can be used to run files and all other stuff. First, you need to setup password less login using ssh-keys between your host and other servers:
Howto Linux / UNIX setup SSH with DSA public key authentication (password less login)
Howto use multiple SSH keys for password less login
The host will run a script, it will login to each system and it will remove files. Here is a sample script to kick start development:
Code:
#!/bin/bash
SERVERS="box1 box2 box3"
for b in $SERVERS
do
ssh user@$b /bin/rm /path/to/file
done
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