let $n \in \mathbb{N}$. Is is possible to find a sequence $S = \{ s_1, \dots, s_{n+k} \}$ ($k \leq n$) with a polynomial algorithm, so that for every pair $(x,y) \in S \times S$, the products $x \cdot y$ are pariwise distinct? Also $s_i \in S$ should be polynomial bounded with respect to $n$.
Regards,
Kreschew