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 $\displaystyle n \geq 1$ for which $\displaystyle 1! + 2! + ... + n!$ is a perfect square. (Hint: Determine the possibilities for the units digit of a perfect square.)

Using the hint:

$\displaystyle 0^2 = 0$

$\displaystyle 1^2 = 1$

$\displaystyle 2^2 = 4$

$\displaystyle 3^2 = 9$

$\displaystyle 4^2 = 16$

$\displaystyle 5^2 = 25$

$\displaystyle 6^2 = 36$

$\displaystyle 7^2 = 49$

$\displaystyle 8^2 = 64$

$\displaystyle 9^2 = 81$

$\displaystyle 10^2 = 100$

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

Then I'm just lost....