There are three (base-ten) 38-digit squares that can be split (somewhere) in such a way that (the difference between the two parts)2 is the original number. One of them is the square of 3636363636363636365:
Square: 36363636363636363652 = 13223140495867768604958677685950413225
Split: (here, into two 19-digit parts) 1322314049586776860 ' 4958677685950413225
Subtract: 4958677685950413225 - 1322314049586776860 = 3636363636363636365
What are the other two solutions?