Find all integral solutions of the equation .
My attempt: The equation can be rewritten as .
Can someone please tell me how to proceed?
I noticed that
May be rewritten as (quite unusual form)
I don't have a clue whether there can be a slightest use of this though, sorry...
Then , so it follows from (1) that is always too small to be a square root for
Next, , and the only integers for which this is not positive are and . For all other integers, is positive, and it follows from (3) that is too large to be a square root of
Thus, unless or , the only possible candidate for an integral square root of is , and it follows from (2) that this solution will only work if
Therefore the only values of that might give solutions to the problem are and . If then , which is not a square. But the other three values of give the solutions to the problem, namely .