Question 112
Let $a_{1}, \ldots, a_{2019}$ positive integers. Show that there is equivalence between: (i) there is a real $x$ such that for all $i \in \{1, \ldots, 2019\}$, we have: $a_{i}=\lfloor i x\rfloor$ (II) for all $i, j \in \{1, \ldots, 2019\}$ checking $i+j \leqslant 2019$, ON A: $a_{i}+a_{j} \leqslant a_{i+j} \leqslant a_{i}+a_{j}+1$.