This is Theorem 1, p. 530 in paper [1] by Pheidas.
Reference
[1] Thanases Pheidas, "An undecidability result for power series rings of positive characteristics. II.An undecidability result for power series rings of positive characteristics. II." Proceedings of the American Mathematical Society 100, 526-530526–530 (1987), MR891158, Zbl 0664.03008.