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Define the $\, n\times n\,$ matrix $\, A = \{a_{i, j}\}_{i, j=1}^n \,$ where $\, a_{i, j} = \binom{n}{j-i}x^n + \binom{n}{i-j}y^n. \,$ The matrix $A$ is a special Toeplitz matrix. Let $\, p(x, y) := \det(A-I).\,$ Since $\, x + y - 1 \,$ is a factor, then also $\, z x + w y - 1 \,$ is a factor where $\, z, w \,$ are any two $\,n-$th roots of unity and there are $\,n^2\,$ of them.

Define the $\, n\times n\,$ matrix $\, A = \{a_{i, j}\}_{i, j=1}^n \,$ where $\, a_{i, j} = \binom{n}{j-i}x^n + \binom{n}{i-j}y^n. \,$ The matrix $A$ is a special Toeplitz matrix. Let $\, p(x, y) := \det(A-I).\,$ Since $\, x + y - 1 \,$ is a factor, then also $\, z x + w y - 1 \,$ is a factor where $\, z, w \,$ are any pair of $\,n$th roots of unity and there are $\,n^2\,$ pairs.

Define the $\, n\times n\,$ matrix $\, A = \{a_{i, j}\}_{i, j=1}^n \,$ where $\, a_{i, j} = \binom{n}{j-i}x^n + \binom{n}{i-j}y^n. \,$ The matrix $A$ is almost a circulant matrix. Let $\, p(x, y) := \det(A-I).\,$ Since $\, x + y - 1 \,$ is a factor, then also $\, z x + w y - 1 \,$ is a factor where $\, z, w \,$ are any two $\,n-$th roots of unity and there are $\,n^2\,$ of them.

Define the $\, n\times n\,$ matrix $\, A = \{a_{i, j}\}_{i, j=1}^n \,$ where $\, a_{i, j} = \binom{n}{j-i}x^n + \binom{n}{i-j}y^n. \,$ The matrix $A$ is a special Toeplitz matrix. Let $\, p(x, y) := \det(A-I).\,$ Since $\, x + y - 1 \,$ is a factor, then also $\, z x + w y - 1 \,$ is a factor where $\, z, w \,$ are any two $\,n-$th roots of unity and there are $\,n^2\,$ of them.

Define the $\, n\times n\,$ matrix $\, A = \{a_{i, j}\}_{i, j=1}^n \,$ where $\, a_{i, j} = \binom{n}{j-i}x^n + \binom{n}{i-j}y^n. \,$ The matrix $A$ is almost a circulant matrix. Let $\, p(x, y) := \det(A-I).\,$ Since $\, x + y - 1 \,$ is a factor, then also $\, z x + w y - 1 \,$ is a factor where $\, z, w \,$ are any two $\,n-$th roots of unity and there are $\,n^2\,$ of them.

Define the $\, n\times n\,$ matrix $\, A = \{a_{i, j}\}_{i, j=1}^n \,$ where $\, a_{i, j} = \binom{n}{j-i}x^n + \binom{n}{i-j}y^n. \,$ The matrix $A$ is almost a circulant matrix. Let $\, p(x, y) := \det(A-I).\,$ Since $\, x + y - 1 \,$ is a factor, then also $\, z x + w y - 1 \,$ is a factor where $\, z, w \,$ are any two $\,n-$th roots of unity and there are $\,n^2\,$ of them.