A Kaprekar number is a positive integer \(n\) such that \(n^2\) can be split into two parts that sum to \(n\) — where the right part may have leading zeros but must be nonzero.
Example: \(297^2 = 88209\). Split as 88 and 209: \(88 + 209 = 297\). ✓
The first few Kaprekar numbers: 1, 9, 45, 55, 99, 297, 703, 999, 2223, 2728, 4879, 4950.
Named after D. R. Kaprekar, an Indian recreational mathematician famous for several number-theoretic discoveries including this one and the famous Kaprekar's constant 6174 (the unique fixed point of a 4-digit subtractive routine).