103. Digits and Squares. What is the smallest square of an integer that ends with the longest sequence of identical digits?

If the longest sequence of identical digits were five, for example, the number 24677777 would fit (if it were the smallest square, but this is not true). Zero is not considered a valid digit.
103. If the square of an integer ends in repeating digits, then these digits can only be 4, as in the case of \(144=12^{2}\). However, the number of such repeating digits cannot exceed three; therefore, the answer is the number \(1444=38^{2}\).