The deadline of this homework is on Monday, 26th of April, 00:00:00 UTC+2.

This week's homework will test your grasp of some of the basic concepts of Python programming. You will have to solve three tasks involving concepts covered in the lecture. As always, you will pass the homework if the pytest passes both on your local system and online for all tasks.

There are three tasks on which you will need to work, distributed across three files:

• digsum.py: Calculate the digit sum of a given int
• fibonacci.py: Calculate the nth Fibonacci number
• findfib.py: Find the first Fibonacci number whose digit sum is larger than 42

If you are using a conda environment, do not forget to activate it first by running conda activate [ENVIRONMENT-NAME] before testing your code.

You can also test your implementation for each task separately using the commands pytest test_digsum.py -vv, pytest test_fibonacci.py -vv and pytest test_findfib.py -vv (the -vv flag will include some more information in the output of the test). In case you lose track which functions pass and which do not, use pytest --tb=no -vv.

You are not allowed to import any libraries for this week's tasks, pure Python code should suffice.

You can also have a look at the test files test_digsum.py, test_fibonacci.py and test_findfib.py if you are unsure about what has to be done. However, in some cases the test files intentionally contain obscuring techniques that ensure that you cannot just look in there for the solution. This is the case e.g. in test_findfib.py.

In the file digsum.py, write a function that for any given non-negative int returns its digit sum, so for e.g. 1234 it should return 10, since 1 + 2 + 3 + 4 = 10.

Hint: You will need to convert between the data types int and str for this task.

In the file fibonacci.py, write a function that returns the nth Fibonacci number. If you do not know what a Fibonacci number is, you can look it up on Wikipedia.

In short, the nth Fibonacci number is defined recursively as follows:

With start values defined as:

Hint: You do not necessarily have to implement this as a recursive function - a simple while-loop can be sufficient.

In the file findfib.py, write a function that determines the first Fibonacci number whose digit sum is larger than 42. For this, you may use the functions digsum and fibonacci that you defined earlier - they are already imported for your convenience.