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Let p>3 be a prime and (. p) be the Legendre symbol. For any integer d with p d and any positive integer m, Sun introduced the determinants Tₘ (d, p) = (i²+dj²) ᵐ (i²+dj²p) ₁ ₈, ₉ (-₁) /₂, and Dₚ^ (m) = (i²-j²) ᵐ (i²-j²p) ₁ ₈, ₉ (-₁) /₂. In this paper, we obtain some properties of Tₘ (d, p) and Dₚ^ (m) for some m. We also confirm some related conjectures posed by Zhi-Wei Sun.
Ren et al. (Fri,) studied this question.