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In this paper, we study arithmetic properties of certain determinants involving powers of i²+cij+dj², where c and d are integers. For example, for any odd integer n>1 with (dn) =-1 we prove that (i²+cij+dj²n) ₀ ₈, ₉ ₍-₁ is divisible by (n) ², where (n) is the Jacobi symbol and is Euler's totient function. This confirms a previous conjecture of the second author.
She et al. (Fri,) studied this question.
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