Add Kaprekar number checker to special_numbers

maths/special_numbers/kaprekar_number.py

@@ -0,0 +1,37 @@
+def is_kaprekar_number(n: int) -> bool:
+    """
+    Determine whether a number is a Kaprekar number (excluding powers of 10).
+
+    A Kaprekar number is a positive number n such that:
+    n^2 = q * 10^m + r, for some m >= 1, q >= 0, 0 <= r < 10^m,
+    and n = q + r, with the restriction that n is not a power of 10.
+
+    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
+        >>> is_kaprekar_number(1)
+        True
+    """
+    if n == 1:
+        return True
+    if n <= 0 or (n % 10 == 0 and n == 10 ** len(str(n))):
+        return False  # Disallow powers of 10 (e.g., 10, 100)
+
+    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 False