Write a python function that takes a positive integer n as an argument. This function will return the number of positive integers less than n that are co-prime to n. Co-prime Numbers: Two numbers are coprime to each other if they don't have any common divisor except 1.

Implement the following function: Code should be written in python.

The following requirments that weren't mentioned for solving the following Python Code below: The provided code for alphabet, test_dups, test_miss, and histogram. Your implementation of the has_duplicates function. A loop that outputs duplicate information for each string in test_dups. Your implementation of the missing_letters function. A loop that outputs missing letters for each string in test_miss. Write a function called missing_letters that takes a string parameter and returns a new string with all the letters of the alphabet that are not in the argument string. The letters in the returned string should be in alphabetical order. Your implementation should use a histogram from the histogram function. It should also use the global variable alphabet. It should use this global variable directly, not through an argument or a local copy. It should loop over the letters in alphabet to determine which are missing from the input parameter. The function missing_letters should...

Write a function "gcDivisor" that takes two positive int "k" and "m" and returns the greatest common divisor of these two positive integers. Using recusion in python3.

Write a recursive function that takes as a parameter a nonnegative integer and generates the following pattern of stars. If the nonnegative integer is 4, the pattern generated is as follows: **** *** ** * * ** *** **** Also, write a program that prompts the user to enter the number of lines in the pattern and uses the recursive function to generate the pattern. For example, specifying 4 as the number of lines generates the preceding pattern.