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This question is answered (affirmatively and somewhat more generally) in the following paper: Chat Yin Ho, Projective planes with a regular collineation group and a question about powers of a prime, J. Algebra 154 (1993), no. 1, 141–151. The proof there uses the ring of Eisenstein integers. (The issue is available online via Open Access).

This question is answered (affirmatively and somewhat more generally) in the following paper: Chat Yin Ho, Projective planes with a regular collineation group and a question about powers of a prime, J. Algebra 154 (1993), no. 1, 141–151. The proof there uses the ring of Eisenstein integers. (The issue is available online via Open Access).

This precise question is answered (affirmatively) in the following paper: Chat Yin Ho, Projective planes with a regular collineation group and a question about powers of a prime, J. Algebra 154 (1993), no. 1, 141–151. The proof there uses the ring of Eisenstein integers. (The issue is available online via Open Access).

This question is answered (affirmatively and somewhat more generally) in the following paper: Chat Yin Ho, Projective planes with a regular collineation group and a question about powers of a prime, J. Algebra 154 (1993), no. 1, 141–151. The proof there uses the ring of Eisenstein integers. (The issue is available online via Open Access).

This precise question is answered in the following paper: Chat Yin Ho, Projective planes with a regular collineation group and a question about powers of a prime, J. Algebra 154 (1993), no. 1, 141–151. The proof there uses the ring of Eisenstein integers.

This precise question is answered (affirmatively) in the following paper: Chat Yin Ho, Projective planes with a regular collineation group and a question about powers of a prime, J. Algebra 154 (1993), no. 1, 141–151. The proof there uses the ring of Eisenstein integers. (The issue is available online via Open Access).