Size of the largest sum-free subset of $[n]^3$, $[n]^4$, and $[n]^5$

Abstract: We determine the density of the largest sum-free subset of the lattice cube ${1, 2, \dots, n}<sup>d$ for $d \in {3, 4, 5}$. This solves a conjecture of Cameron and Aydinian in dimensions $3$, $4$, and $5$.