8 Prove that lim $(\sqrt{n^2+n}-n) = \frac{1}{2}$ 7 Does bounded and continuous implies Lipschitz? 5 Prove that if $n$ is a positive integer then $\sqrt{n}+ \sqrt{2}$ is irrational 4 Calculating the class group of $\mathcal{O}_K$, for $K=\mathbb{Q}(\sqrt{7})$? 3 Inequality on lengths and sums of vectors $\left\lVert\sum_i \vec{a_i}\right\rVert \le \sum_i \left\lVert \vec{a_i}\right\rVert$

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 +30 Prove that lim $(\sqrt{n^2+n}-n) = \frac{1}{2}$ +10 Show that the form $w$ is closed but not exact +30 Does bounded and continuous implies Lipschitz? +10 Graph (or manifold) Lipschitz satisfy the sphere (ball) condition?

### Questions (8)

 9 Is there an irreducible projective hypersurface such that its complement has zero Euler characteristic? 3 Can you have solution for the equation $|\nabla f|^2=f\,\Delta f$, for a homogeneous polynomial $f$ with $\deg(f)>2$? 2 Lipschitz manifold and semi-algebraic is Lipschitz graph? 1 Extension of a map $g:\overline{B_1^n}\to \mathbb{R}^2$ 0 First Betti number of a finite union of circles

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 16 Gromov-Hausdorff convergence to a circle