maths: add Kaprekar number implementation

maths/special_numbers/kaprekar_number.py

@@ -0,0 +1,56 @@
+"""
+== Kaprekar Number ==
+A number n is a Kaprekar number if its square can be split into two parts
+(left and right) that add up to n, where the right part is non-zero.
+
+Examples: 1, 9, 45, 55, 99, 297, 703, 999, 2223, 4950, 5050, 7272, 9999
+Reference: https://en.wikipedia.org/wiki/Kaprekar_number
+"""
+
+
+def is_kaprekar(number: int) -> bool:
+    """
+    Returns True if number is a Kaprekar number, False otherwise.
+
+    >>> is_kaprekar(1)
+    True
+    >>> is_kaprekar(9)
+    True
+    >>> is_kaprekar(45)
+    True
+    >>> is_kaprekar(55)
+    True
+    >>> is_kaprekar(10)
+    False
+    >>> is_kaprekar(0)
+    False
+    >>> is_kaprekar(-1)
+    False
+    >>> is_kaprekar(2223)
+    True
+    >>> is_kaprekar(1.5)
+    Traceback (most recent call last):
+        ...
+    TypeError: Input value of [number=1.5] must be an integer
+    """
+    if not isinstance(number, int):
+        msg = f"Input value of [number={number}] must be an integer"
+        raise TypeError(msg)
+    if number < 1:
+        return False
+    if number == 1:
+        return True
+    square = number**2
+    digits = len(str(square))
+    for split in range(1, digits):
+        right = square % (10**split)
+        left = square // (10**split)
+        if right > 0 and left + right == number:
+            return True
+    return False
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()