Assignment:
There are 130 cabinets in a row in a warehouse. The first worker to arrive opens the door of every cabinet. The next employee visits every other door and closes it. The third arrives and visits every third door and opens it if it's closed, or closes it if opened. The fourth visits every fourth door and follows the same procedure. This continues until all 130 employees have arrived, with the 130th employee visiting only door 130.
Which doors, if any, are open after the last employee arrives?
Provide complete and step by step solution for the question and show calculations and use formulas.