- Assuming you already have key setup for your machine.

#!/bin/bash
 
hostlist=( 'alpha.lan' 'beta.lan' 'gamma.lan' 'delta.lan' 'epsilon.lan' )
# get number of elements in the array
chost=${#hostlist[@]}
 
 
for (( i=0;i<$chost;i++)); do
    echo ${hostlist[${i}]}
	file=`cat /dev/urandom|od -N4 -An -i`
	scp ${hostlist[${i}]}:.ssh/authorized_keys /tmp/$file
	if cat /tmp/$file | grep "`cat mike.pub`"
		then
		echo "Key already exists"
		rm -rf /tmp/$file
	else
		cat mike.pub >> /tmp/$file
		if cat /tmp/$file | grep "`cat mike.pub`"
			then
				echo "Key Successfully Adde"
				scp /tmp/$file ${hostlist[${i}]}:.ssh/authorized_keys
			else
				echo "Failed to add key for host \"${hostlist[${i}]}\" Check manually."
		fi
	fi
done