#### BinomialExpansion Putnam

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Let $n$ be a positive integer. Show that the smallest integer that is larger than $(1+\sqrt{3})^{2n}$ is divisible by $2^{n+1}$.

Let $m$ and $n$ be positive integers. Show that $$\frac{(m+n)!}{(m+n)^{m+n}}<\frac{m!}{m^m}\frac{n!}{n^n}$$