I've been racking my brain out for the last two days on this problem, but I don't even have the slightest clue on how to approach this problem. Could anybody point me in the right direction please?

Q: Find the values of for which is a perfect square. (Hint: Determine the possibilities for the units digit of a perfect square.)

Using the hint:

This leads to a pattern: 0 1 4 9 6 5 6 9 4 1 0

Then I'm just lost....