show that $h(k)=\left \lfloor{\frac{k}{m}}\right \rfloor \mod m$ is a bad hash function where $m$ is prime

Question

A "good" hash function should make use of all slots with equal frequency. In this case the ammount of slots is given with $m$.

Also keys which are similar should be distributed as broadly as possible.

Any ideas how to approach this excercise?

Answer 1

Hint. Take for instance $m = 5$ and consider the numbers $0, 1, \ldots, 29$. Then you will have $10$ numbers in slot $0$, but only $5$ numbers in slots $1$, $2$, $3$, $4$. Thus taking $k \bmod m$ would give a much better result.