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Guo","submitted_at":"2014-12-18T07:07:22Z","abstract_excerpt":"The multi-variable Schmidt polynomials are defined by $$ S_n^{(r)}(x_0,\\ldots,x_n):=\\sum_{k=0}^n {n+k \\choose 2k}^{r}{2k\\choose k} x_k. $$ We prove that, for any positive integers $m$, $n$, $r$, and $\\varepsilon=\\pm 1$, all the coefficients in the polynomial $$ \\sum_{k=0}^{n-1}\\varepsilon^k(2k+1) S_k^{(r)}(x_0,\\ldots,x_k)^m $$ are multiples of $n$. 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