Add Kaprekar number checker to special_numbers

maths/special_numbers/kaprekar_number.py

@@ -0,0 +1,35 @@
+def is_kaprekar_number(n: int) -> bool:
+    """
+    Determine whether a number is a Kaprekar number.
+
+    A Kaprekar number is one where the square can be split into parts
+    that sum to the original number.
+
+    Args:
+        n (int): The number to check.
+
+    Returns:
+        bool: True if it's a Kaprekar number, else False.
+
+    Examples:
+        >>> is_kaprekar_number(45)
+        True
+        >>> is_kaprekar_number(9)
+        True
+        >>> is_kaprekar_number(10)
+        False
+    """
+    square = str(n**2)
+    for i in range(1, len(square)):
+        left, right = square[:i], square[i:]
+        if int(right) == 0:
+            continue
+        if n == int(left or "0") + int(right):
+            return True
+    return n == 1
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()