Flajolet-Martin Algorithm : question about use of certain hash functions
However, I can't seem to figure the answer to the second exercice ? Is it simply to choose 'a' and 'b' in a certain manner ? or are these functions not good to generate equally randomly numbers with trailing 0s and no trailing 0s ?


You have the right idea. I believe what the question is trying to suggest is that this hash function has a problem with certain values of $a$ and $b$. Consider, in particular, $a = 16$. What will happen to the hash function in that case? How many possible values are there?

So, to pick a good value of $a$, we should probably make sure that $a = 16$ is not allowed. $a = 8$ is not good either. What do you suggest is a good choice for $a$?