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Let $\mathcal{S}$ be the set of all nonconstant monic polynomials $P$ with integer coefficients satisfying $P(\sqrt{3}+\sqrt{2})=$ $P(\sqrt{3}-\sqrt{2})$. If $Q$ is an element of $\mathcal{S}$ with minimal degree, compute the only possible value of $Q(10)-Q(0)$. | 890 |
Let $r$ be the remainder when $2017^{2025!}-1$ is divided by 2025!. Compute $\frac{r}{2025!}$. (Note that $2017$ is prime.) | \frac{1311}{2017} |
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