Let us call "fine" the 2n-digit number if it is exact square itself and the two numbers represented by its first n digits (first digit may not be zero) and last n digits (first digit may be zero, but it may not be zero itself) are exact squares also. a) Find all two- and four-digit fine numbers. b) Is there any six-digit fine number? c) Prove that there exists 20-digit fine number. d) Prove that there exist at least ten 100-digit fine numbers. e) Prove that there exists 30-digit fine number. Perfect Squarenumber theory