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The n-dimensional finite projective space, P G(n, q), admits a cyclic model, in which the set of points of P G(n, q) is identified with the elements of the group Z q n +q n−1 +···+q+1. It was proved by Hall (1974, Math. Centre Tracts, 57, 1–26) that in the cyclic model of P G(2, q), the additive inverse of a line is a conic. The following generalization of(More)