Proving that collision is less likely if the table size is prime in case modulo arithmetic is used
It requires Theorem 31.20 on Page 927 from the CLRS (for which there is a proof of the theorem on the same page) that "if $d = gcd(a, n)$ then $\langle a\rangle = \langle d \rangle = \{0, d, 2d, \ldots, ((n/d) -1)d\}$ in $\mathbb{Z}_n$, and thus $|\langle a\rangle| = n/d$"

But it's Corollary will be more useful to the proof:
"The equation $ax \equiv b \mod n$ is solvable for the unknown $x$ if and only if $d|b$, where $d = gcd(a, n)$"

These conclusions will be the core of the proof.