Add new algorithm (is_K_power_of_N)

Author: rudrakshtank

bit_manipulation/is_K_power_of_N.py

@@ -1,39 +1,65 @@
+The error message `Syntax Error @ 1:1. tokenizer error: '`' is not a valid character in this position\` indicates that the Python parser is encountering an invalid character right at the beginning of the file.
+
+The character causing the issue is the backtick symbol (`` ` ``) which seems to have been included at the very start of the code block. This is not a valid character to start a Python statement.
+
+Here is the corrected code. It is identical to the previous version, but without the leading backtick, making it syntactically correct.
+
+```python
+"""
+Author  : Your Name
+Date    : August 1, 2025
+
+Task:
+Given two positive integers, n and k, determine if k is a power of n.
+
+Implementation notes: Use a loop to repeatedly divide k by n.
+For a number k to be a power of n, it must be possible to reduce k
+to 1 by repeatedly dividing by n without any remainder.
+For example, 8 is a power of 2 because:
+8 / 2 = 4
+4 / 2 = 2
+2 / 2 = 1
+The final result is 1.
+"""
+
+
 def is_k_power_of_n(n: int, k: int) -> bool:
     """
-    Given two positive integers, n and k, this function determines if k
-    is a power of n. A number k is a power of n if k = n^x for some
-    non-negative integer x.
+    Return True if k is a power of n or False otherwise.
 
     >>> is_k_power_of_n(2, 8)
     True
-    >>> is_k_power_of_n(3, 10)
-    False
+    >>> is_k_power_of_n(3, 9)
+    True
     >>> is_k_power_of_n(5, 5)
     True
-    >>> is_k_power_of_n(10, 1000)
+    >>> is_k_power_of_n(2, 1)
     True
+    >>> is_k_power_of_n(3, 10)
+    False
+    >>> is_k_power_of_n(2, 6)
+    False
     >>> is_k_power_of_n(4, 2)
     False
     >>> is_k_power_of_n(1, 1)
     True
     >>> is_k_power_of_n(1, 5)
     False
-    >>> is_k_power_of_n(0, 16)
+    >>> is_k_power_of_n(-2, 8)
     Traceback (most recent call last):
         ...
     ValueError: Both n and k must be positive integers
     >>> is_k_power_of_n(2, -8)
     Traceback (most recent call last):
         ...
     ValueError: Both n and k must be positive integers
-    >>> is_k_power_of_n(2, 'a')
+    >>> is_k_power_of_n(2.5, 8)
     Traceback (most recent call last):
         ...
     TypeError: n and k must be integers
     """
     if not isinstance(n, int) or not isinstance(k, int):
         raise TypeError("n and k must be integers")
-
     if n <= 0 or k <= 0:
         raise ValueError("Both n and k must be positive integers")