Let

. Check that

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

.