### Questions (24)

 4 When is $4n^4+1$ prime? 4 Induction proof about entries of powers of strictly upper triangular matrix 3 $n=2^k-1$ iff ${n \choose 1}, {n \choose 2}, …, {n \choose n-1}$ are odd 2 $\alpha = \sqrt2 + \sqrt3 \in V$ then $\dim_\Bbb Q V=4$ 2 Applying Jensen's inequality to show $\sqrt[n]{y_1…y_n} \ \leq \frac{y_1+…+y_n}{n}$

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 +5 Induction proof about entries of powers of strictly upper triangular matrix +10 $\alpha = \sqrt2 + \sqrt3 \in V$ then $\dim_\Bbb Q V=4$ +5 Prove simple closed curves $f$'s exist, so $\Gamma = C-\sum_{i=1}^{k}{f_i}$ satisfies $\int_{\Gamma}{\frac{z^3e^{1/z}}{(z^2 + z + 1)(z^2 + 1)}dz}=0$ -2 Prove $d$ and $d'=\frac{d}{1+d}$ are equivalent metrics

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