Integral automorphisms of affine spaces over finite fields

A permutation of the point set of the affine space $${{\mathrm{AG}}}(n,q)$$AG(n,q) is called an integral automorphism if it preserves the integral distance defined among the points. In this paper, we complete the classification of the integral automorphisms of $${{\mathrm{AG}}}(n,q)$$AG(n,q) for $$n\ge 3$$n≥3.