Problem 1183

3. Let the hashing function be $h(K) \equiv K(\bmod m)$, with $0 \leqslant h(K)<m$, and let the probing sequence for collision resolution be $h_{j}(K) \equiv h(K)+j q(\bmod m)$, $0 \leqslant h_{j}(K)<m$, for $j=1,2, \ldots, m-1$. Show that all memory locations are probed
a) if $m$ is prime and $1 \leqslant q \leqslant m-1$.
b) if $m=2^{r}$ and $q$ is odd.