add is_k_power_of_n.py to bit manipulation

Author: rudrakshtank

bit_manipulation/is_k_power_of_n.py

@@ -0,0 +1,59 @@
+def is_power(base: int, number: int) -> bool:
+    """
+    Checks if a given integer `number` is a power of another integer `base`.
+
+    This function determines if there exists an integer x such that base^x = number.
+    It handles positive integers only and raises an error for non-positive inputs.
+    For more information, see: https://en.wikipedia.org/wiki/Power_of_two
+
+    Args:
+        base: The base integer (must be a positive integer).
+        number: The number to check if it's a power of base
+            (must be a positive integer).
+
+    Returns:
+        True if number is a power of base, False otherwise.
+
+    Raises:
+        ValueError: If base or number are not positive integers.
+
+    Examples:
+    >>> is_power(2, 8)
+    True
+    >>> is_power(3, 81)
+    True
+    >>> is_power(10, 1)
+    True
+    >>> is_power(5, 120)
+    False
+    >>> is_power(1, 1)
+    True
+    >>> is_power(1, 5)
+    False
+    >>> is_power(0, 5)
+    Traceback (most recent call last):
+        ...
+    ValueError: Both base and number must be positive integers
+    >>> is_power(4, -16)
+    Traceback (most recent call last):
+        ...
+    ValueError: Both base and number must be positive integers
+    """
+    if base <= 0 or number <= 0:
+        raise ValueError("Both base and number must be positive integers")
+
+    if base == 1:
+        return number == 1
+
+    # Repeatedly divide number by base until it's no longer divisible.
+    while number % base == 0:
+        number //= base
+
+    # If number has been reduced to 1, it was a power of base.
+    return number == 1
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()