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In the $m$-dimensional affine space $AG(m,q)$ over the finite field$\mathbb{F}_q$ of odd order $q$, the analogous of the Euclidean distance givesrise to a graph $\mathfrak{G}_{m,q}$ where vertices are the points of $AG(m,q)$and two vertices are adjacent if their (formal) squared Euclidean distance is asquare in $\mathbb{F}_q$ (including the zero). In 2009, Kurz and Meyer made theconjecture that if $m$ is even then $\mathfrak{G}_{m,q}$ is a strongly regulargraph. In this paper we prove their conjecture.

Strongly regular graphs from integral point sets in even dimensional affine spaces over finite fields