As usual, write in your diary as you do the following exercises.

Optional this time, required soon, and highly recommended. Write your homework in LaTeX and include your Python code and testing in the document. Use my solution to homework 2 (www.cs.umb.edu/~eb/480/hw02/) as a model - start with that TeX file, keep all the TeX preliminaries and the structure, then edit the content starting with \begin{document}. If you read my content you can see how to get all the cool formatting.

If you've used TeX before, this is a requirement now. If you haven't, it's time to try to get started. This is not "extra work" since TeX is one of the software tools for mathematics this course is meant to teach you. To get started you will need a TeX distribution (that's like getting python for your computer) and a TeX editor (think of that as an IDE for TeX, like pycharm for Python). You can find what you need at the (TeX resources link on the course home page.

1. Find out how to display the documentation Python allows for modules and functions using the syntax

   def myfunction(parameters):
       """ Documentation here, 
       with lines delimited by triple quotation marks
       """
       # function body
       return something
   

2. Write and test the function

   def eulerphi( b ):
       """ Given a positive integer b, 
       returns a list of the integers between 1 and b
       that are relatively prime to b.
       
       For example, eulerphi(15) returns the list
           [1,2,4,7,8,11,13,14]
   
       Use the function gcd from the fractions library.
       """
   

3. Write and test the function

   def primeslessthan(b):
       """ Return a list of the primes less than 
           the positive integer b.
       """
   

   Since b won't be very large (say no bigger than 1000) you can call eratosthenes.py for this, or create a file of primes (easy from the web) and read it.

4. Write, test and time the function

   def fsf(n, b):
       """ Find and return the smallest factor of n:
   
       Get the list L Lof primes less than or equal to b.
   
       See if any of the primes in L is a factor of n.
   
       Calculate M, the product of the primes in L,
   
       Loop up to sqrt(n) testing only possible factors of 
       the form kM + j for j in eulerphi(M) with k = 1, 2, ...
       """