  Hegarty conjectured for $n\neq 2, 3, 5, 7$ that $\mathbb{Z}/n\mathbb{Z}$ has
a permutation which destroys all arithmetic progressions mod $n$. For $n\ge
n_0$, Hegarty and Martinsson demonstrated that $\mathbb{Z}/n\mathbb{Z}$ has an
arithmetic-progression destroying permutation. However $n_0\approx 1.4\times
10^{14}$ and thus resolving the conjecture in full remained out of reach of any
computational techniques. However, this paper using constructions modeled after
those used by Elkies and Swaminathan for the case of $\mathbb{Z}/p\mathbb{Z}$
with $p$ being prime, establish the conjecture in full. Furthermore our results
do not rely on the fact that it suffices to study when $n<n_0$ and thus our
results completely independent of the proof given by Hegarty and Martinsson.
