grandes-ecoles 2016 Q8

grandes-ecoles · France · x-ens-maths1__mp Proof Existence Proof
Let $V \geqslant 0$ be a real number.
8a. Give an example of an integer simplex in $\mathbb{R}^2$ with volume greater than or equal to $V$ and having no interior integer points.
8b. Give an example of an integer simplex in $\mathbb{R}^3$ with volume greater than or equal to $V$ whose only integer points are the vertices.
Let $V \geqslant 0$ be a real number.

8a. Give an example of an integer simplex in $\mathbb{R}^2$ with volume greater than or equal to $V$ and having no interior integer points.

8b. Give an example of an integer simplex in $\mathbb{R}^3$ with volume greater than or equal to $V$ whose only integer points are the vertices.