Ubuntu 16.04 lts lost administrator rights bash: /etc/profile: Permission denied

There is no need to execute chmod at all when using sudo to edit a file, although you shouldn't use sudo gedit (rather sudo -H gedit for example)

Since you didn't change permissions recursively, you can fix the problem fairly easily.

Boot a live session (for example, Ubuntu bootable USB you use for installation, or System Rescue. If you don't have one, you can make one using another computer or even buy one). If using an Ubuntu live USB, select **Try Ubuntu without installing".

In the live environment, identify the (afflicted) root partition on the disk using sudo fdisk -l

It will probably the biggest partition and it will be labelled "Linux filesystem". Something like /dev/sda1 or maybe /dev/mmcblk0p2.

Mount the root partition, using the proper name instead of sdXY

sudo mount /dev/sdxY /mnt

Check it was the right partition:

ls /mnt

Should output something you'd expect to see in /, roughly like:

bin    dev   lib64       mnt   root  snap      sys  var
boot   etc   lost+found  opt   run   srv       tmp  
cdrom  home  lib         media       proc      sbin usr

If it looks right:

cd /mnt
sudo chmod 755 etc
sudo chmod 755 etc/pm
sudo chmod 755 etc/pm/config.d
cd

Then you can unmount the partition and reboot into your system as normal

sudo umount /mnt
reboot