Add new algorithm (is_K_power_of_N) to bit manipulation

bit_manipulation/is_K_power_of_N.py

@@ -0,0 +1,78 @@
+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:
+    """
+    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, 9)
+    True
+    >>> is_k_power_of_n(5, 5)
+    True
+    >>> 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(-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(2.5, 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")
+
+    if n == 1:
+        return k == 1
+
+    while k % n == 0:
+        k //= n
+    return k == 1
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+```