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Sun. For any positive integer $n\\equiv3\\pmod4$, we show that $$(6,1)_n=[6,1]_n=(3,2)_n=[3,2]_n=0$$ and $$(4,2)_n=(8,8)_n=(3,3)_n=(21,112)_n=0$$ as conjectured by Sun, where $$(c,d)_n=\\bigg|\\left(\\frac{i^2+cij+dj^2}n\\right)\\bigg|_{1\\le i,j\\le n-1}$$ and $$[c,d]_n=\\bigg|\\left(\\frac{i^2+cij+dj^2}n\\right)\\bigg|_{0\\le i,j\\le n-1}$$ with $(\\frac{\\cdot}n)$ the Jacobi symbol. 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