  The Moore spectrum $\mathrm{M}_p(i)$ is the cofiber of the $p^{i}$ map on the
sphere spectrum. For a fixed $p$ and $n$, we find a lower bound on $i$ for
which $\mathrm{M}_p(i)$ is guaranteed to be $n$-fold associative. This bound
depends on the stable homotopy groups of spheres.
