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The ring of integer-valued polynomials on the matrix ring $M_n(D)$, denoted ${\\rm Int}_K(M_n(D))$, consists of those polynomials in $K[x]$ that map matrices in $M_n(D)$ back to $M_n(D)$ under evaluation. It has been known for some time that ${\\rm Int}_{\\mathbb{Q}}(M_n(\\mathbb{Z}))$ is not integrally closed. 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